2461:
114:. If a wire joins the battery to one bulb, to the next bulb, to the next bulb, to the next bulb, then back to the battery in one continuous loop, the bulbs are said to be in series. If each bulb is wired to the battery in a separate loop, the bulbs are said to be in parallel. If the four light bulbs are connected in series, the same current flows through all of them and the voltage drop is 3 volts across each bulb, which may not be sufficient to make them glow. If the light bulbs are connected in parallel, the currents through the light bulbs combine to form the current in the battery, while the voltage drop is 12 volts across each bulb and they all glow.
2214:
4027:
1587:
1152:
3402:
2709:
143:
33:
4187:. Lithium-ion rechargeable batteries (particularly laptop batteries) are often connected in parallel to increase the ampere-hour rating. Some solar electric systems have batteries in parallel to increase the storage capacity; a close approximation of total amp-hours is the sum of all amp-hours of in-parallel batteries.
5216:
A common application of series circuit in consumer electronics is in batteries, where several cells connected in series are used to obtain a convenient operating voltage. Two disposable zinc cells in series might power a flashlight or remote control at 3 volts; the battery pack for a hand-held power
1707:
When there are more than two inductors, the mutual inductance between each of them and the way the coils influence each other complicates the calculation. For a larger number of coils the total combined inductance is given by the sum of all mutual inductances between the various coils including the
3592:
2404:
1487:
2896:
4171:
If the cells of a battery are connected in parallel, the battery voltage will be the same as the cell voltage, but the current supplied by each cell will be a fraction of the total current. For example, if a battery comprises four identical cells connected in parallel and delivers a current of 1
2468:
If two or more components are connected in parallel, they have the same difference of potential (voltage) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities. The same voltage is applied to all circuit components
1703:
However, in some situations, it is difficult to prevent adjacent inductors from influencing each other as the magnetic field of one device couples with the windings of its neighbors. This influence is defined by the mutual inductance M. For example, if two inductors are in series, there are two
5239:
Series resistance can also be applied to the arrangement of blood vessels within a given organ. Each organ is supplied by a large artery, smaller arteries, arterioles, capillaries, and veins arranged in series. The total resistance is the sum of the individual resistances, as expressed by the
2183:
so that the last two groups can be combined. The first three terms represent the sum of the self-inductances of the various coils. The formula is easily extended to any number of series coils with mutual coupling. The method can be used to find the self-inductance of large coils of wire of any
117:
In a series circuit, every device must function for the circuit to be complete. If one bulb burns out in a series circuit, the entire circuit is broken. In parallel circuits, each light bulb has its own circuit, so all but one light could be burned out, and the last one will still function.
5042:
70:
Components connected in series are connected along a single "electrical path", and each component has the same electric current through it, equal to the current through the network. The voltage across the network is equal to the sum of the voltages across each component.
2119:
5207:
3407:
2219:
1302:
2714:
4865:
3819:
More than three inductors become more complex and the mutual inductance of each inductor on each other inductor and their influence on each other must be considered. For three coils, there are three mutual inductances
4885:
3381:
The relations for total conductance and resistance stand in a complementary relationship: the expression for a series connection of resistances is the same as for parallel connection of conductances, and vice versa.
2660:
4139:
3377:
1699:
1264:
4654:
4584:
3227:
1957:
5049:
3694:
1138:
67:) or an electrical network (e.g. resistors in series) is a matter of perspective. This article will use "component" to refer to a two-terminal "object" that participates in the series/parallel networks.
4005:
3800:
depends on how the magnetic fields influence each other. For two equal tightly coupled coils the total inductance is close to that of every single coil. If the polarity of one coil is reversed so that
4176:, the current supplied by each cell will be 0.25 ampere. If the cells are not identical in voltage, cells with higher voltages will attempt to charge those with lower ones, potentially damaging them.
4735:
2975:
1566:
3812:. However, if the inductances are not equal and the coils are tightly coupled there can be near short circuit conditions and high circulating currents for both positive and negative values of
3034:
3154:
2213:
1151:
1037:
2548:
1586:
107:
across each component. In a parallel circuit, the voltage across each of the components is the same, and the total current is the sum of the currents flowing through each component.
3776:
4026:
3070:
4468:
in series the current through them will be the same and
Kirchhoff's Voltage Law says that the voltage across them is the sum of the voltages across each conductance, that is,
4361:
3401:
2708:
4515:
4410:
4304:
3596:
If the inductors are situated in each other's magnetic fields, this approach is invalid due to mutual inductance. If the mutual inductance between two coils in parallel is
3736:
2184:
cross-sectional shape by computing the sum of the mutual inductance of each turn of wire in the coil with every other turn since in such a coil all turns are in series.
956:-coupled. The current in a series circuit goes through every component in the circuit. Therefore, all of the components in a series connection carry the same current.
1299:
presents a reciprocal quantity to resistance. Total conductance of a series circuits of pure resistances, therefore, can be calculated from the following expression:
3899:
3872:
3845:
2181:
2151:
1949:
1922:
1895:
1868:
1841:
1814:
1787:
1760:
1733:
4740:
4466:
4439:
4251:
4224:
3103:
2702:
5339:
are the resistances of the renal, hepatic, and other arteries respectively. The total resistance is less than the resistance of any of the individual arteries.
3919:
3798:
3265:
700:
2564:
5537:
4032:
3587:{\displaystyle L=\left(\sum _{i=1}^{n}{1 \over L_{i}}\right)^{-1}=\left({1 \over L_{1}}+{1 \over L_{2}}+{1 \over L_{3}}+\dots +{1 \over L_{n}}\right)^{-1}.}
3270:
2399:{\displaystyle C=\left(\sum _{i=1}^{n}{1 \over C_{i}}\right)^{-1}=\left({1 \over C_{1}}+{1 \over C_{2}}+{1 \over C_{3}}+\dots +{1 \over C_{n}}\right)^{-1}.}
1592:
1482:{\displaystyle G=\left(\sum _{i=1}^{n}{1 \over G_{i}}\right)^{-1}=\left({1 \over G_{1}}+{1 \over G_{2}}+{1 \over G_{3}}+\dots +{1 \over G_{n}}\right)^{-1}.}
1157:
4589:
2891:{\displaystyle R=\left(\sum _{i=1}^{n}{1 \over R_{i}}\right)^{-1}=\left({1 \over R_{1}}+{1 \over R_{2}}+{1 \over R_{3}}+\dots +{1 \over R_{n}}\right)^{-1}}
4522:
1708:
mutual inductance of each given coil with itself, which is termed self-inductance or simply inductance. For three coils, there are six mutual inductances
673:
103:
In a series circuit, the current that flows through each of the components is the same, and the voltage across the circuit is the sum of the individual
685:
3161:
3603:
1052:
3804:
is negative, then the parallel inductance is nearly zero or the combination is almost non-inductive. It is assumed in the "tightly coupled" case
3927:
78:
across it, equal to the voltage across the network. The current through the network is equal to the sum of the currents through each component.
2452:
contains six 2-volt cells connected in series. Some vehicles, such as trucks, have two 12 volt batteries in series to feed the 24-volt system.
2470:
4663:
4143:
The working voltage of a parallel combination of capacitors is always limited by the smallest working voltage of an individual capacitor.
2903:
1494:
936:
705:
2704:
of each component and take the reciprocal of the sum. Total resistance will always be less than the value of the smallest resistance:
2993:
715:
5552:
5037:{\displaystyle R\equiv R_{1}\parallel R_{2}\equiv \left(R_{1}^{-1}+R_{2}^{-1}\right)^{-1}\equiv {\frac {R_{1}R_{2}}{R_{1}+R_{2}}}}
3108:
977:
5224:
trains. For example, if the supply voltage was 600 volts there might be eight 70-volt bulbs in series (total 560 volts) plus a
2488:
2464:
Comparison of effective resistance, inductance and capacitance of two resistors, inductors and capacitors in series and parallel
2448:. If the cells are connected in series, the voltage of the battery will be the sum of the cell voltages. For example, a 12 volt
5373:
4658:
This equation can be rearranged slightly, though this is a special case that will only rearrange like this for two components.
3397:
of non-coupled inductors in parallel is equal to the reciprocal of the sum of the reciprocals of their individual inductances:
963:
causes the entire circuit to "open" or stop operating. For example, if even one of the light bulbs in an older-style string of
540:
555:
177:
953:
2469:
connected in parallel. The total current is the sum of the currents through the individual components, in accordance with
3740:
3039:
2114:{\displaystyle L=\left(M_{11}+M_{22}+M_{33}\right)+\left(M_{12}+M_{13}+M_{23}\right)+\left(M_{21}+M_{31}+M_{32}\right)}
1147:
The total resistance of two or more resistors connected in series is equal to the sum of their individual resistances:
5202:{\displaystyle R_{1}\parallel R_{2}\parallel R_{3}\equiv {\frac {R_{1}R_{2}R_{3}}{R_{1}R_{2}+R_{1}R_{3}+R_{2}R_{3}}}.}
4311:
5527:
167:
4471:
4366:
4260:
435:
959:
A series circuit has only one path through which its current can flow. Opening or breaking a series circuit at any
1049:
In a series circuit, the voltage is the sum of the voltage drops of the individual components (resistance units).
5363:
350:
5353:
3267:
is reciprocal to resistance, the expression for total conductance of a parallel circuit of resistors is simply:
5398:
3158:
The components divide the current according to their reciprocal resistances, so, in the case of two resistors,
929:
695:
172:
97:
60:
59:. The resulting electrical network will have two terminals, and itself can participate in a series or parallel
5046:
This simplifies expressions that would otherwise become complicated by expansion of the terms. For instance:
5388:
1704:
possible equivalent inductances depending on how the magnetic fields of both inductors influence each other.
710:
415:
82:
5573:
575:
315:
182:
2412:(the reciprocal of capacitance), the total series elastance equals the sum of each capacitor's elastance.
305:
5393:
5348:
4196:
868:
743:
640:
615:
535:
17:
2460:
368:
5233:
922:
883:
410:
400:
340:
335:
275:
74:
Components connected in parallel are connected along multiple paths, and each component has the same
420:
4257:, the voltage across them is the same and from Kirchhoff's current law (KCL) the total current is
853:
355:
5383:
5221:
3701:
967:
burns out or is removed, the entire string becomes inoperable until the faulty bulb is replaced.
960:
733:
260:
250:
245:
4879:
858:
828:
2674:
2206:
1296:
680:
450:
225:
44:
5228:
to drop the remaining 40 volts. Series circuits for train lighting were superseded, first by
5519:
3075:
2670:
2441:
964:
778:
465:
455:
405:
395:
96:. Many circuits can be analyzed as a combination of series and parallel circuits, along with
5281:. The total resistance of this parallel arrangement is expressed by the following equation:
3877:
3850:
3823:
2156:
2126:
1927:
1900:
1873:
1846:
1819:
1792:
1765:
1738:
1711:
4444:
4417:
4229:
4202:
3081:
2680:
2445:
903:
803:
768:
520:
385:
285:
270:
205:
142:
8:
5378:
4156:
2425:
863:
843:
838:
645:
630:
515:
485:
380:
310:
48:
5270:. The largest proportion of resistance in this series is contributed by the arterioles.
1582:
of non-coupled inductors in series is equal to the sum of their individual inductances:
5274:
3904:
3783:
3250:
738:
478:
280:
240:
111:
560:
5523:
5474:
5470:
5447:
5443:
5408:
5368:
4875:
3901:. This is best handled by matrix methods and summing the terms of the inverse of the
1491:
For a special case of two conductances in series, the total conductance is equal to:
798:
898:
813:
773:
763:
650:
605:
588:
505:
440:
210:
134:
5413:
5217:
tool might contain a dozen lithium-ion cells wired in series to provide 48 volts.
5403:
5358:
5229:
4874:
The value of two components in parallel is often represented in equations by the
833:
758:
753:
620:
495:
460:
320:
220:
873:
4184:
793:
788:
610:
500:
425:
375:
325:
298:
255:
230:
200:
193:
37:
4860:{\displaystyle G={\frac {G_{1}G_{2}G_{3}}{G_{1}G_{2}+G_{1}G_{3}+G_{2}G_{3}}}.}
2900:
For only two resistances, the unreciprocated expression is reasonably simple:
2193:
5567:
908:
893:
878:
818:
530:
445:
430:
345:
330:
235:
2990:
equal resistances in parallel, the reciprocal sum expression simplifies to:
110:
Consider a very simple circuit consisting of four light bulbs and a 12-volt
5542:
2558:
888:
783:
748:
690:
625:
545:
510:
390:
265:
104:
4199:
the rules for combining conductance can be deducted. For two conductances
88:
A circuit composed solely of components connected in series is known as a
4180:
4015:
2449:
2202:
808:
660:
490:
152:
4019:
3394:
2655:{\displaystyle I=\sum _{i=1}^{n}I_{i}=V\sum _{i=1}^{n}{1 \over R_{i}}.}
1579:
525:
4134:{\displaystyle C=\sum _{i=1}^{n}C_{i}=C_{1}+C_{2}+C_{3}\cdots +C_{n}.}
3372:{\displaystyle G=\sum _{i=1}^{n}G_{i}=G_{1}+G_{2}+G_{3}\cdots +G_{n}.}
1694:{\displaystyle L=\sum _{i=1}^{n}L_{i}=L_{1}+L_{2}+L_{3}\cdots +L_{n}.}
1259:{\displaystyle R=\sum _{i=1}^{n}R_{i}=R_{1}+R_{2}+R_{3}\cdots +R_{n}.}
1041:
In a series circuit, the current is the same for all of the elements.
40:(such as a battery, or in this case a cell) and three resistance units
4649:{\displaystyle {\frac {1}{G}}={\frac {1}{G_{1}}}+{\frac {1}{G_{2}}}.}
2409:
2205:
of capacitors in series is equal to the reciprocal of the sum of the
2198:
848:
823:
635:
157:
63:. Whether a two-terminal "object" is an electrical component (e.g. a
4579:{\displaystyle {\frac {I}{G}}={\frac {I}{G_{1}}}+{\frac {I}{G_{2}}}}
4159:; the circuit carries current if at least one switch is closed. See
5225:
3390:
3236:
2429:
2428:; the circuit only carries current if all switches are closed. See
1575:
600:
595:
215:
64:
4022:
in parallel is equal to the sum of their individual capacitances:
4160:
570:
75:
32:
5538:"Resistor combinations: How many values using 1K ohm resistors?"
5478:
5451:
4586:
which in turn gives the formula for the equivalent conductance,
1870:. There are also the three self-inductances of the three coils:
4173:
4152:
2421:
655:
162:
92:; likewise, one connected completely in parallel is known as a
3222:{\displaystyle {\frac {I_{1}}{I_{2}}}={\frac {R_{2}}{R_{1}}}.}
5278:
5277:. Each organ is supplied by an artery that branches off the
3689:{\displaystyle L={\frac {L_{1}L_{2}-M^{2}}{L_{1}+L_{2}-2M}}}
1133:{\displaystyle V=\sum _{i=1}^{n}V_{i}=I\sum _{i=1}^{n}R_{i}}
4179:
Parallel-connected batteries were widely used to power the
4000:{\displaystyle v_{i}=\sum _{j}L_{i,j}{\frac {di_{j}}{dt}}}
5442:. Vol. I and II (Combined international ed.).
81:
The two preceding statements are equivalent, except for
5438:
Resnick, Robert; Halliday, David (1966). "Chapter 32".
5052:
4888:
4743:
4666:
4592:
4525:
4474:
4447:
4420:
4369:
4314:
4263:
4232:
4205:
4035:
3930:
3907:
3880:
3853:
3826:
3786:
3743:
3704:
3606:
3410:
3273:
3253:
3164:
3111:
3084:
3042:
2996:
2906:
2717:
2683:
2567:
2491:
2222:
2201:
follow the same law using the reciprocals. The total
2159:
2129:
1960:
1930:
1903:
1876:
1849:
1822:
1795:
1768:
1741:
1714:
1595:
1497:
1305:
1160:
1055:
980:
4730:{\displaystyle G={\frac {G_{1}G_{2}}{G_{1}+G_{2}}}.}
2970:{\displaystyle R={\frac {R_{1}R_{2}}{R_{1}+R_{2}}}.}
2557:
The current in each individual resistor is found by
1561:{\displaystyle G={\frac {G_{1}G_{2}}{G_{1}+G_{2}}}.}
5220:Series circuits were formerly used for lighting in
4519:Substituting Ohm's law for conductance then gives,
5201:
5036:
4859:
4729:
4648:
4578:
4509:
4460:
4433:
4404:
4355:
4298:
4245:
4218:
4133:
3999:
3913:
3893:
3866:
3839:
3792:
3770:
3730:
3688:
3586:
3371:
3259:
3221:
3148:
3097:
3064:
3028:
2969:
2890:
2696:
2654:
2542:
2398:
2175:
2145:
2113:
1943:
1916:
1889:
1862:
1835:
1808:
1781:
1754:
1727:
1693:
1560:
1481:
1258:
1132:
1031:
3231:An old term for devices connected in parallel is
5565:
952:are sometimes referred to as current-coupled or
5437:
3029:{\displaystyle {\frac {1}{R}}=N{\frac {1}{R}}.}
5433:
5431:
5429:
4308:Substituting Ohm's law for conductances gives
930:
2485:, the voltage is the same for all elements.
5426:
3149:{\displaystyle I_{i}={\frac {V}{R_{i}}}\,.}
1032:{\displaystyle I=I_{1}=I_{2}=\cdots =I_{n}}
5273:Parallel resistance is illustrated by the
2543:{\displaystyle V=V_{1}=V_{2}=\dots =V_{n}}
937:
923:
141:
83:exchanging the role of voltage and current
5458:
4190:
3924:The pertinent equations are of the form:
3142:
5513:
4878:, two vertical lines (â„), borrowing the
4363:and the equivalent conductance will be,
4166:
2459:
31:
3393:follow the same law, in that the total
1578:follow the same law, in that the total
686:Electromagnetism and special relativity
14:
5566:
5374:Network analysis (electrical circuits)
2435:
550:
5550:
5490:
5488:
5464:
4880:parallel lines notation from geometry
2664:
706:Maxwell equations in curved spacetime
5494:
5469:(International ed.). New York:
2979:This sometimes goes by the mnemonic
2455:
565:
3235:, such as multiple connections for
1142:
24:
5507:
5499:. Board Review Series. p. 74.
5485:
4737:For three conductances in series,
3771:{\displaystyle L={\frac {L+M}{2}}}
2561:. Factoring out the voltage gives
2209:of their individual capacitances:
121:
25:
5585:
3065:{\displaystyle R={\frac {R}{N}}.}
5516:The Circuit Designer's Companion
4356:{\displaystyle GV=G_{1}V+G_{2}V}
4025:
3400:
3242:
2707:
2212:
1585:
1288:denotes resistance in a series.
1150:
5364:Equivalent impedance transforms
5211:
4009:
3078:in a component with resistance
5551:Grotz, Bernhard (2018-01-04).
5399:Topology (electrical circuits)
4510:{\displaystyle V=V_{1}+V_{2}.}
4405:{\displaystyle G=G_{1}+G_{2}.}
4299:{\displaystyle I=I_{1}+I_{2}.}
3600:, the equivalent inductor is:
3385:
1291:
13:
1:
5467:Circuits, Devices and Systems
5419:
5389:Series-parallel partial order
4146:
3247:Since electrical conductance
2187:
711:Relativistic electromagnetism
3816:, which can cause problems.
2552:
2476:
1570:
27:Types of electrical circuits
7:
5394:Series and parallel springs
5349:Anti-parallel (electronics)
5342:
4869:
3921:matrix (3Ă3 in this case).
3731:{\displaystyle L_{1}=L_{2}}
2673:of all components, add the
2415:
10:
5590:
5557:Mechanik der FlĂŒssigkeiten
2191:
1044:
970:
436:LiĂ©nardâWiechert potential
2194:Capacitor § Networks
701:Mathematical descriptions
411:Electromagnetic radiation
401:Electromagnetic induction
341:Magnetic vector potential
336:Magnetic scalar potential
4197:Kirchhoff's circuit laws
3808:is very nearly equal to
36:A series circuit with a
5384:Series-parallel duality
5222:electric multiple units
3105:, use Ohm's law again:
2471:Kirchhoff's current law
251:Electrostatic induction
246:Electrostatic discharge
5514:Williams, Tim (2005).
5203:
5038:
4861:
4731:
4650:
4580:
4511:
4462:
4435:
4406:
4357:
4300:
4247:
4220:
4191:Combining conductances
4135:
4062:
4001:
3915:
3895:
3894:{\displaystyle M_{23}}
3868:
3867:{\displaystyle M_{13}}
3841:
3840:{\displaystyle M_{12}}
3794:
3772:
3732:
3690:
3588:
3443:
3373:
3300:
3261:
3223:
3150:
3099:
3066:
3030:
2971:
2892:
2750:
2698:
2656:
2631:
2594:
2544:
2465:
2400:
2255:
2177:
2176:{\displaystyle M_{ji}}
2147:
2146:{\displaystyle M_{ij}}
2115:
1945:
1944:{\displaystyle M_{33}}
1918:
1917:{\displaystyle M_{22}}
1891:
1890:{\displaystyle M_{11}}
1864:
1863:{\displaystyle M_{32}}
1837:
1836:{\displaystyle M_{31}}
1810:
1809:{\displaystyle M_{21}}
1783:
1782:{\displaystyle M_{23}}
1756:
1755:{\displaystyle M_{13}}
1729:
1728:{\displaystyle M_{12}}
1695:
1622:
1562:
1483:
1338:
1297:Electrical conductance
1279:denotes "series", and
1260:
1187:
1134:
1119:
1082:
1033:
681:Electromagnetic tensor
41:
5553:"Strömungswiderstand"
5520:Butterworth-Heinemann
5465:Smith, R. J. (1966).
5204:
5039:
4862:
4732:
4651:
4581:
4512:
4463:
4461:{\displaystyle G_{2}}
4436:
4434:{\displaystyle G_{1}}
4414:For two conductances
4407:
4358:
4301:
4248:
4246:{\displaystyle G_{2}}
4221:
4219:{\displaystyle G_{1}}
4136:
4042:
4002:
3916:
3896:
3869:
3842:
3795:
3773:
3733:
3691:
3589:
3423:
3374:
3280:
3262:
3224:
3151:
3100:
3098:{\displaystyle R_{i}}
3067:
3031:
2972:
2893:
2730:
2699:
2697:{\displaystyle R_{i}}
2657:
2611:
2574:
2545:
2463:
2446:electrochemical cells
2401:
2235:
2178:
2148:
2116:
1946:
1919:
1892:
1865:
1838:
1811:
1784:
1757:
1730:
1696:
1602:
1563:
1484:
1318:
1261:
1167:
1135:
1099:
1062:
1034:
965:Christmas tree lights
674:Covariant formulation
466:Synchrotron radiation
406:Electromagnetic pulse
396:Electromagnetic field
35:
5354:Combining impedances
5240:following equation:
5050:
4886:
4741:
4664:
4590:
4523:
4472:
4445:
4418:
4367:
4312:
4261:
4230:
4203:
4033:
3928:
3905:
3878:
3851:
3824:
3784:
3741:
3702:
3604:
3408:
3271:
3251:
3162:
3109:
3082:
3040:
2994:
2904:
2715:
2681:
2565:
2489:
2220:
2157:
2127:
1958:
1928:
1901:
1874:
1847:
1820:
1793:
1766:
1739:
1712:
1593:
1495:
1303:
1266:Here, the subscript
1158:
1053:
978:
716:Stressâenergy tensor
641:Reluctance (complex)
386:Displacement current
98:other configurations
51:can be connected in
5574:Electrical circuits
5495:Costanzo, Linda S.
5379:Resistance distance
4965:
4944:
4167:Cells and batteries
4155:in parallel form a
2677:of the resistances
2444:is a collection of
2436:Cells and batteries
2408:Equivalently using
631:Magnetomotive force
516:Electromotive force
486:Alternating current
421:Jefimenko equations
381:Cyclotron radiation
49:electrical networks
5275:circulatory system
5199:
5034:
4948:
4927:
4857:
4727:
4646:
4576:
4507:
4458:
4431:
4402:
4353:
4296:
4243:
4216:
4131:
3997:
3953:
3911:
3891:
3864:
3837:
3790:
3768:
3728:
3686:
3584:
3369:
3257:
3219:
3146:
3095:
3062:
3036:and therefore to:
3026:
2967:
2888:
2694:
2669:To find the total
2652:
2540:
2466:
2396:
2173:
2143:
2111:
1941:
1914:
1887:
1860:
1833:
1806:
1779:
1752:
1725:
1691:
1558:
1479:
1256:
1130:
1029:
479:Electrical network
316:Gauss magnetic law
281:Static electricity
241:Electric potential
112:automotive battery
42:
5409:Wheatstone bridge
5369:Hydraulic analogy
5194:
5032:
4876:parallel operator
4852:
4722:
4641:
4621:
4601:
4574:
4554:
4534:
3995:
3944:
3914:{\displaystyle L}
3793:{\displaystyle M}
3766:
3684:
3565:
3539:
3519:
3499:
3459:
3260:{\displaystyle G}
3214:
3187:
3140:
3057:
3021:
3005:
2962:
2872:
2846:
2826:
2806:
2766:
2647:
2456:Parallel circuits
2424:in series form a
2377:
2351:
2331:
2311:
2271:
1553:
1460:
1434:
1414:
1394:
1354:
947:
946:
646:Reluctance (real)
616:Gyratorâcapacitor
561:Resonant cavities
451:Maxwell equations
16:(Redirected from
5581:
5560:
5547:
5533:
5501:
5500:
5492:
5483:
5482:
5462:
5456:
5455:
5435:
5338:
5329:
5320:
5311:
5269:
5230:motor-generators
5208:
5206:
5205:
5200:
5195:
5193:
5192:
5191:
5182:
5181:
5169:
5168:
5159:
5158:
5146:
5145:
5136:
5135:
5125:
5124:
5123:
5114:
5113:
5104:
5103:
5093:
5088:
5087:
5075:
5074:
5062:
5061:
5043:
5041:
5040:
5035:
5033:
5031:
5030:
5029:
5017:
5016:
5006:
5005:
5004:
4995:
4994:
4984:
4979:
4978:
4970:
4966:
4964:
4956:
4943:
4935:
4917:
4916:
4904:
4903:
4866:
4864:
4863:
4858:
4853:
4851:
4850:
4849:
4840:
4839:
4827:
4826:
4817:
4816:
4804:
4803:
4794:
4793:
4783:
4782:
4781:
4772:
4771:
4762:
4761:
4751:
4736:
4734:
4733:
4728:
4723:
4721:
4720:
4719:
4707:
4706:
4696:
4695:
4694:
4685:
4684:
4674:
4655:
4653:
4652:
4647:
4642:
4640:
4639:
4627:
4622:
4620:
4619:
4607:
4602:
4594:
4585:
4583:
4582:
4577:
4575:
4573:
4572:
4560:
4555:
4553:
4552:
4540:
4535:
4527:
4516:
4514:
4513:
4508:
4503:
4502:
4490:
4489:
4467:
4465:
4464:
4459:
4457:
4456:
4440:
4438:
4437:
4432:
4430:
4429:
4411:
4409:
4408:
4403:
4398:
4397:
4385:
4384:
4362:
4360:
4359:
4354:
4349:
4348:
4333:
4332:
4305:
4303:
4302:
4297:
4292:
4291:
4279:
4278:
4252:
4250:
4249:
4244:
4242:
4241:
4225:
4223:
4222:
4217:
4215:
4214:
4140:
4138:
4137:
4132:
4127:
4126:
4111:
4110:
4098:
4097:
4085:
4084:
4072:
4071:
4061:
4056:
4029:
4006:
4004:
4003:
3998:
3996:
3994:
3986:
3985:
3984:
3971:
3969:
3968:
3952:
3940:
3939:
3920:
3918:
3917:
3912:
3900:
3898:
3897:
3892:
3890:
3889:
3873:
3871:
3870:
3865:
3863:
3862:
3846:
3844:
3843:
3838:
3836:
3835:
3815:
3811:
3807:
3803:
3799:
3797:
3796:
3791:
3777:
3775:
3774:
3769:
3767:
3762:
3751:
3737:
3735:
3734:
3729:
3727:
3726:
3714:
3713:
3695:
3693:
3692:
3687:
3685:
3683:
3673:
3672:
3660:
3659:
3649:
3648:
3647:
3635:
3634:
3625:
3624:
3614:
3599:
3593:
3591:
3590:
3585:
3580:
3579:
3571:
3567:
3566:
3564:
3563:
3551:
3540:
3538:
3537:
3525:
3520:
3518:
3517:
3505:
3500:
3498:
3497:
3485:
3474:
3473:
3465:
3461:
3460:
3458:
3457:
3445:
3442:
3437:
3404:
3378:
3376:
3375:
3370:
3365:
3364:
3349:
3348:
3336:
3335:
3323:
3322:
3310:
3309:
3299:
3294:
3266:
3264:
3263:
3258:
3228:
3226:
3225:
3220:
3215:
3213:
3212:
3203:
3202:
3193:
3188:
3186:
3185:
3176:
3175:
3166:
3155:
3153:
3152:
3147:
3141:
3139:
3138:
3126:
3121:
3120:
3104:
3102:
3101:
3096:
3094:
3093:
3071:
3069:
3068:
3063:
3058:
3050:
3035:
3033:
3032:
3027:
3022:
3014:
3006:
2998:
2981:product over sum
2976:
2974:
2973:
2968:
2963:
2961:
2960:
2959:
2947:
2946:
2936:
2935:
2934:
2925:
2924:
2914:
2897:
2895:
2894:
2889:
2887:
2886:
2878:
2874:
2873:
2871:
2870:
2858:
2847:
2845:
2844:
2832:
2827:
2825:
2824:
2812:
2807:
2805:
2804:
2792:
2781:
2780:
2772:
2768:
2767:
2765:
2764:
2752:
2749:
2744:
2711:
2703:
2701:
2700:
2695:
2693:
2692:
2665:Resistance units
2661:
2659:
2658:
2653:
2648:
2646:
2645:
2633:
2630:
2625:
2604:
2603:
2593:
2588:
2549:
2547:
2546:
2541:
2539:
2538:
2520:
2519:
2507:
2506:
2483:parallel circuit
2405:
2403:
2402:
2397:
2392:
2391:
2383:
2379:
2378:
2376:
2375:
2363:
2352:
2350:
2349:
2337:
2332:
2330:
2329:
2317:
2312:
2310:
2309:
2297:
2286:
2285:
2277:
2273:
2272:
2270:
2269:
2257:
2254:
2249:
2216:
2182:
2180:
2179:
2174:
2172:
2171:
2152:
2150:
2149:
2144:
2142:
2141:
2123:By reciprocity,
2120:
2118:
2117:
2112:
2110:
2106:
2105:
2104:
2092:
2091:
2079:
2078:
2061:
2057:
2056:
2055:
2043:
2042:
2030:
2029:
2012:
2008:
2007:
2006:
1994:
1993:
1981:
1980:
1950:
1948:
1947:
1942:
1940:
1939:
1923:
1921:
1920:
1915:
1913:
1912:
1896:
1894:
1893:
1888:
1886:
1885:
1869:
1867:
1866:
1861:
1859:
1858:
1842:
1840:
1839:
1834:
1832:
1831:
1815:
1813:
1812:
1807:
1805:
1804:
1788:
1786:
1785:
1780:
1778:
1777:
1761:
1759:
1758:
1753:
1751:
1750:
1734:
1732:
1731:
1726:
1724:
1723:
1700:
1698:
1697:
1692:
1687:
1686:
1671:
1670:
1658:
1657:
1645:
1644:
1632:
1631:
1621:
1616:
1589:
1567:
1565:
1564:
1559:
1554:
1552:
1551:
1550:
1538:
1537:
1527:
1526:
1525:
1516:
1515:
1505:
1488:
1486:
1485:
1480:
1475:
1474:
1466:
1462:
1461:
1459:
1458:
1446:
1435:
1433:
1432:
1420:
1415:
1413:
1412:
1400:
1395:
1393:
1392:
1380:
1369:
1368:
1360:
1356:
1355:
1353:
1352:
1340:
1337:
1332:
1287:
1278:
1265:
1263:
1262:
1257:
1252:
1251:
1236:
1235:
1223:
1222:
1210:
1209:
1197:
1196:
1186:
1181:
1154:
1143:Resistance units
1139:
1137:
1136:
1131:
1129:
1128:
1118:
1113:
1092:
1091:
1081:
1076:
1038:
1036:
1035:
1030:
1028:
1027:
1009:
1008:
996:
995:
939:
932:
925:
606:Electric machine
589:Magnetic circuit
551:Parallel circuit
541:Network analysis
506:Electric current
441:London equations
286:Triboelectricity
276:Potential energy
145:
135:Electromagnetism
126:
125:
94:parallel circuit
21:
5589:
5588:
5584:
5583:
5582:
5580:
5579:
5578:
5564:
5563:
5536:
5530:
5510:
5508:Further reading
5505:
5504:
5493:
5486:
5463:
5459:
5436:
5427:
5422:
5404:Voltage divider
5359:Current divider
5345:
5337:
5331:
5328:
5322:
5319:
5313:
5310:
5303:
5296:
5289:
5282:
5268:
5261:
5254:
5247:
5241:
5214:
5187:
5183:
5177:
5173:
5164:
5160:
5154:
5150:
5141:
5137:
5131:
5127:
5126:
5119:
5115:
5109:
5105:
5099:
5095:
5094:
5092:
5083:
5079:
5070:
5066:
5057:
5053:
5051:
5048:
5047:
5025:
5021:
5012:
5008:
5007:
5000:
4996:
4990:
4986:
4985:
4983:
4971:
4957:
4952:
4936:
4931:
4926:
4922:
4921:
4912:
4908:
4899:
4895:
4887:
4884:
4883:
4872:
4845:
4841:
4835:
4831:
4822:
4818:
4812:
4808:
4799:
4795:
4789:
4785:
4784:
4777:
4773:
4767:
4763:
4757:
4753:
4752:
4750:
4742:
4739:
4738:
4715:
4711:
4702:
4698:
4697:
4690:
4686:
4680:
4676:
4675:
4673:
4665:
4662:
4661:
4635:
4631:
4626:
4615:
4611:
4606:
4593:
4591:
4588:
4587:
4568:
4564:
4559:
4548:
4544:
4539:
4526:
4524:
4521:
4520:
4498:
4494:
4485:
4481:
4473:
4470:
4469:
4452:
4448:
4446:
4443:
4442:
4425:
4421:
4419:
4416:
4415:
4393:
4389:
4380:
4376:
4368:
4365:
4364:
4344:
4340:
4328:
4324:
4313:
4310:
4309:
4287:
4283:
4274:
4270:
4262:
4259:
4258:
4237:
4233:
4231:
4228:
4227:
4210:
4206:
4204:
4201:
4200:
4193:
4185:portable radios
4169:
4149:
4122:
4118:
4106:
4102:
4093:
4089:
4080:
4076:
4067:
4063:
4057:
4046:
4034:
4031:
4030:
4012:
3987:
3980:
3976:
3972:
3970:
3958:
3954:
3948:
3935:
3931:
3929:
3926:
3925:
3906:
3903:
3902:
3885:
3881:
3879:
3876:
3875:
3858:
3854:
3852:
3849:
3848:
3831:
3827:
3825:
3822:
3821:
3813:
3809:
3805:
3801:
3785:
3782:
3781:
3752:
3750:
3742:
3739:
3738:
3722:
3718:
3709:
3705:
3703:
3700:
3699:
3668:
3664:
3655:
3651:
3650:
3643:
3639:
3630:
3626:
3620:
3616:
3615:
3613:
3605:
3602:
3601:
3597:
3572:
3559:
3555:
3550:
3533:
3529:
3524:
3513:
3509:
3504:
3493:
3489:
3484:
3483:
3479:
3478:
3466:
3453:
3449:
3444:
3438:
3427:
3422:
3418:
3417:
3409:
3406:
3405:
3388:
3360:
3356:
3344:
3340:
3331:
3327:
3318:
3314:
3305:
3301:
3295:
3284:
3272:
3269:
3268:
3252:
3249:
3248:
3245:
3208:
3204:
3198:
3194:
3192:
3181:
3177:
3171:
3167:
3165:
3163:
3160:
3159:
3134:
3130:
3125:
3116:
3112:
3110:
3107:
3106:
3089:
3085:
3083:
3080:
3079:
3049:
3041:
3038:
3037:
3013:
2997:
2995:
2992:
2991:
2955:
2951:
2942:
2938:
2937:
2930:
2926:
2920:
2916:
2915:
2913:
2905:
2902:
2901:
2879:
2866:
2862:
2857:
2840:
2836:
2831:
2820:
2816:
2811:
2800:
2796:
2791:
2790:
2786:
2785:
2773:
2760:
2756:
2751:
2745:
2734:
2729:
2725:
2724:
2716:
2713:
2712:
2688:
2684:
2682:
2679:
2678:
2667:
2641:
2637:
2632:
2626:
2615:
2599:
2595:
2589:
2578:
2566:
2563:
2562:
2555:
2534:
2530:
2515:
2511:
2502:
2498:
2490:
2487:
2486:
2479:
2458:
2438:
2418:
2384:
2371:
2367:
2362:
2345:
2341:
2336:
2325:
2321:
2316:
2305:
2301:
2296:
2295:
2291:
2290:
2278:
2265:
2261:
2256:
2250:
2239:
2234:
2230:
2229:
2221:
2218:
2217:
2196:
2190:
2164:
2160:
2158:
2155:
2154:
2134:
2130:
2128:
2125:
2124:
2100:
2096:
2087:
2083:
2074:
2070:
2069:
2065:
2051:
2047:
2038:
2034:
2025:
2021:
2020:
2016:
2002:
1998:
1989:
1985:
1976:
1972:
1971:
1967:
1959:
1956:
1955:
1935:
1931:
1929:
1926:
1925:
1908:
1904:
1902:
1899:
1898:
1881:
1877:
1875:
1872:
1871:
1854:
1850:
1848:
1845:
1844:
1827:
1823:
1821:
1818:
1817:
1800:
1796:
1794:
1791:
1790:
1773:
1769:
1767:
1764:
1763:
1746:
1742:
1740:
1737:
1736:
1719:
1715:
1713:
1710:
1709:
1682:
1678:
1666:
1662:
1653:
1649:
1640:
1636:
1627:
1623:
1617:
1606:
1594:
1591:
1590:
1573:
1546:
1542:
1533:
1529:
1528:
1521:
1517:
1511:
1507:
1506:
1504:
1496:
1493:
1492:
1467:
1454:
1450:
1445:
1428:
1424:
1419:
1408:
1404:
1399:
1388:
1384:
1379:
1378:
1374:
1373:
1361:
1348:
1344:
1339:
1333:
1322:
1317:
1313:
1312:
1304:
1301:
1300:
1294:
1286:
1280:
1277:
1271:
1247:
1243:
1231:
1227:
1218:
1214:
1205:
1201:
1192:
1188:
1182:
1171:
1159:
1156:
1155:
1145:
1124:
1120:
1114:
1103:
1087:
1083:
1077:
1066:
1054:
1051:
1050:
1047:
1023:
1019:
1004:
1000:
991:
987:
979:
976:
975:
973:
950:Series circuits
943:
914:
913:
729:
721:
720:
676:
666:
665:
621:Induction motor
591:
581:
580:
496:Current density
481:
471:
470:
461:Poynting vector
371:
369:Electrodynamics
361:
360:
356:Right-hand rule
321:Magnetic dipole
311:BiotâSavart law
301:
291:
290:
226:Electric dipole
221:Electric charge
196:
124:
122:Series circuits
47:components and
28:
23:
22:
15:
12:
11:
5:
5587:
5577:
5576:
5562:
5561:
5548:
5534:
5528:
5509:
5506:
5503:
5502:
5484:
5473:. p. 21.
5457:
5424:
5423:
5421:
5418:
5417:
5416:
5411:
5406:
5401:
5396:
5391:
5386:
5381:
5376:
5371:
5366:
5361:
5356:
5351:
5344:
5341:
5335:
5326:
5317:
5308:
5301:
5294:
5287:
5266:
5259:
5252:
5245:
5213:
5210:
5198:
5190:
5186:
5180:
5176:
5172:
5167:
5163:
5157:
5153:
5149:
5144:
5140:
5134:
5130:
5122:
5118:
5112:
5108:
5102:
5098:
5091:
5086:
5082:
5078:
5073:
5069:
5065:
5060:
5056:
5028:
5024:
5020:
5015:
5011:
5003:
4999:
4993:
4989:
4982:
4977:
4974:
4969:
4963:
4960:
4955:
4951:
4947:
4942:
4939:
4934:
4930:
4925:
4920:
4915:
4911:
4907:
4902:
4898:
4894:
4891:
4871:
4868:
4856:
4848:
4844:
4838:
4834:
4830:
4825:
4821:
4815:
4811:
4807:
4802:
4798:
4792:
4788:
4780:
4776:
4770:
4766:
4760:
4756:
4749:
4746:
4726:
4718:
4714:
4710:
4705:
4701:
4693:
4689:
4683:
4679:
4672:
4669:
4645:
4638:
4634:
4630:
4625:
4618:
4614:
4610:
4605:
4600:
4597:
4571:
4567:
4563:
4558:
4551:
4547:
4543:
4538:
4533:
4530:
4506:
4501:
4497:
4493:
4488:
4484:
4480:
4477:
4455:
4451:
4428:
4424:
4401:
4396:
4392:
4388:
4383:
4379:
4375:
4372:
4352:
4347:
4343:
4339:
4336:
4331:
4327:
4323:
4320:
4317:
4295:
4290:
4286:
4282:
4277:
4273:
4269:
4266:
4240:
4236:
4213:
4209:
4192:
4189:
4168:
4165:
4148:
4145:
4130:
4125:
4121:
4117:
4114:
4109:
4105:
4101:
4096:
4092:
4088:
4083:
4079:
4075:
4070:
4066:
4060:
4055:
4052:
4049:
4045:
4041:
4038:
4011:
4008:
3993:
3990:
3983:
3979:
3975:
3967:
3964:
3961:
3957:
3951:
3947:
3943:
3938:
3934:
3910:
3888:
3884:
3861:
3857:
3834:
3830:
3789:
3765:
3761:
3758:
3755:
3749:
3746:
3725:
3721:
3717:
3712:
3708:
3682:
3679:
3676:
3671:
3667:
3663:
3658:
3654:
3646:
3642:
3638:
3633:
3629:
3623:
3619:
3612:
3609:
3583:
3578:
3575:
3570:
3562:
3558:
3554:
3549:
3546:
3543:
3536:
3532:
3528:
3523:
3516:
3512:
3508:
3503:
3496:
3492:
3488:
3482:
3477:
3472:
3469:
3464:
3456:
3452:
3448:
3441:
3436:
3433:
3430:
3426:
3421:
3416:
3413:
3387:
3384:
3368:
3363:
3359:
3355:
3352:
3347:
3343:
3339:
3334:
3330:
3326:
3321:
3317:
3313:
3308:
3304:
3298:
3293:
3290:
3287:
3283:
3279:
3276:
3256:
3244:
3241:
3218:
3211:
3207:
3201:
3197:
3191:
3184:
3180:
3174:
3170:
3145:
3137:
3133:
3129:
3124:
3119:
3115:
3092:
3088:
3061:
3056:
3053:
3048:
3045:
3025:
3020:
3017:
3012:
3009:
3004:
3001:
2966:
2958:
2954:
2950:
2945:
2941:
2933:
2929:
2923:
2919:
2912:
2909:
2885:
2882:
2877:
2869:
2865:
2861:
2856:
2853:
2850:
2843:
2839:
2835:
2830:
2823:
2819:
2815:
2810:
2803:
2799:
2795:
2789:
2784:
2779:
2776:
2771:
2763:
2759:
2755:
2748:
2743:
2740:
2737:
2733:
2728:
2723:
2720:
2691:
2687:
2666:
2663:
2651:
2644:
2640:
2636:
2629:
2624:
2621:
2618:
2614:
2610:
2607:
2602:
2598:
2592:
2587:
2584:
2581:
2577:
2573:
2570:
2554:
2551:
2537:
2533:
2529:
2526:
2523:
2518:
2514:
2510:
2505:
2501:
2497:
2494:
2478:
2475:
2457:
2454:
2437:
2434:
2417:
2414:
2395:
2390:
2387:
2382:
2374:
2370:
2366:
2361:
2358:
2355:
2348:
2344:
2340:
2335:
2328:
2324:
2320:
2315:
2308:
2304:
2300:
2294:
2289:
2284:
2281:
2276:
2268:
2264:
2260:
2253:
2248:
2245:
2242:
2238:
2233:
2228:
2225:
2189:
2186:
2170:
2167:
2163:
2140:
2137:
2133:
2109:
2103:
2099:
2095:
2090:
2086:
2082:
2077:
2073:
2068:
2064:
2060:
2054:
2050:
2046:
2041:
2037:
2033:
2028:
2024:
2019:
2015:
2011:
2005:
2001:
1997:
1992:
1988:
1984:
1979:
1975:
1970:
1966:
1963:
1938:
1934:
1911:
1907:
1884:
1880:
1857:
1853:
1830:
1826:
1803:
1799:
1776:
1772:
1749:
1745:
1722:
1718:
1690:
1685:
1681:
1677:
1674:
1669:
1665:
1661:
1656:
1652:
1648:
1643:
1639:
1635:
1630:
1626:
1620:
1615:
1612:
1609:
1605:
1601:
1598:
1572:
1569:
1557:
1549:
1545:
1541:
1536:
1532:
1524:
1520:
1514:
1510:
1503:
1500:
1478:
1473:
1470:
1465:
1457:
1453:
1449:
1444:
1441:
1438:
1431:
1427:
1423:
1418:
1411:
1407:
1403:
1398:
1391:
1387:
1383:
1377:
1372:
1367:
1364:
1359:
1351:
1347:
1343:
1336:
1331:
1328:
1325:
1321:
1316:
1311:
1308:
1293:
1290:
1284:
1275:
1255:
1250:
1246:
1242:
1239:
1234:
1230:
1226:
1221:
1217:
1213:
1208:
1204:
1200:
1195:
1191:
1185:
1180:
1177:
1174:
1170:
1166:
1163:
1144:
1141:
1127:
1123:
1117:
1112:
1109:
1106:
1102:
1098:
1095:
1090:
1086:
1080:
1075:
1072:
1069:
1065:
1061:
1058:
1046:
1043:
1026:
1022:
1018:
1015:
1012:
1007:
1003:
999:
994:
990:
986:
983:
972:
969:
945:
944:
942:
941:
934:
927:
919:
916:
915:
912:
911:
906:
901:
896:
891:
886:
881:
876:
871:
866:
861:
856:
851:
846:
841:
836:
831:
826:
821:
816:
811:
806:
801:
796:
791:
786:
781:
776:
771:
766:
761:
756:
751:
746:
741:
736:
730:
727:
726:
723:
722:
719:
718:
713:
708:
703:
698:
696:Four-potential
693:
688:
683:
677:
672:
671:
668:
667:
664:
663:
658:
653:
648:
643:
638:
633:
628:
623:
618:
613:
611:Electric motor
608:
603:
598:
592:
587:
586:
583:
582:
579:
578:
573:
568:
566:Series circuit
563:
558:
553:
548:
543:
538:
536:Kirchhoff laws
533:
528:
523:
518:
513:
508:
503:
501:Direct current
498:
493:
488:
482:
477:
476:
473:
472:
469:
468:
463:
458:
456:Maxwell tensor
453:
448:
443:
438:
433:
428:
426:Larmor formula
423:
418:
413:
408:
403:
398:
393:
388:
383:
378:
376:Bremsstrahlung
372:
367:
366:
363:
362:
359:
358:
353:
348:
343:
338:
333:
328:
326:Magnetic field
323:
318:
313:
308:
302:
299:Magnetostatics
297:
296:
293:
292:
289:
288:
283:
278:
273:
268:
263:
258:
253:
248:
243:
238:
233:
231:Electric field
228:
223:
218:
213:
208:
203:
201:Charge density
197:
194:Electrostatics
192:
191:
188:
187:
186:
185:
180:
175:
170:
165:
160:
155:
147:
146:
138:
137:
131:
130:
129:Articles about
123:
120:
90:series circuit
38:voltage source
26:
9:
6:
4:
3:
2:
5586:
5575:
5572:
5571:
5569:
5558:
5554:
5549:
5545:
5544:
5539:
5535:
5531:
5529:0-7506-6370-7
5525:
5521:
5517:
5512:
5511:
5498:
5491:
5489:
5480:
5476:
5472:
5468:
5461:
5453:
5449:
5445:
5441:
5434:
5432:
5430:
5425:
5415:
5414:Y-Î transform
5412:
5410:
5407:
5405:
5402:
5400:
5397:
5395:
5392:
5390:
5387:
5385:
5382:
5380:
5377:
5375:
5372:
5370:
5367:
5365:
5362:
5360:
5357:
5355:
5352:
5350:
5347:
5346:
5340:
5334:
5325:
5316:
5307:
5300:
5293:
5286:
5280:
5276:
5271:
5265:
5258:
5251:
5244:
5237:
5235:
5231:
5227:
5223:
5218:
5209:
5196:
5188:
5184:
5178:
5174:
5170:
5165:
5161:
5155:
5151:
5147:
5142:
5138:
5132:
5128:
5120:
5116:
5110:
5106:
5100:
5096:
5089:
5084:
5080:
5076:
5071:
5067:
5063:
5058:
5054:
5044:
5026:
5022:
5018:
5013:
5009:
5001:
4997:
4991:
4987:
4980:
4975:
4972:
4967:
4961:
4958:
4953:
4949:
4945:
4940:
4937:
4932:
4928:
4923:
4918:
4913:
4909:
4905:
4900:
4896:
4892:
4889:
4881:
4877:
4867:
4854:
4846:
4842:
4836:
4832:
4828:
4823:
4819:
4813:
4809:
4805:
4800:
4796:
4790:
4786:
4778:
4774:
4768:
4764:
4758:
4754:
4747:
4744:
4724:
4716:
4712:
4708:
4703:
4699:
4691:
4687:
4681:
4677:
4670:
4667:
4659:
4656:
4643:
4636:
4632:
4628:
4623:
4616:
4612:
4608:
4603:
4598:
4595:
4569:
4565:
4561:
4556:
4549:
4545:
4541:
4536:
4531:
4528:
4517:
4504:
4499:
4495:
4491:
4486:
4482:
4478:
4475:
4453:
4449:
4426:
4422:
4412:
4399:
4394:
4390:
4386:
4381:
4377:
4373:
4370:
4350:
4345:
4341:
4337:
4334:
4329:
4325:
4321:
4318:
4315:
4306:
4293:
4288:
4284:
4280:
4275:
4271:
4267:
4264:
4256:
4238:
4234:
4211:
4207:
4198:
4188:
4186:
4183:filaments in
4182:
4177:
4175:
4164:
4162:
4158:
4154:
4144:
4141:
4128:
4123:
4119:
4115:
4112:
4107:
4103:
4099:
4094:
4090:
4086:
4081:
4077:
4073:
4068:
4064:
4058:
4053:
4050:
4047:
4043:
4039:
4036:
4028:
4023:
4021:
4017:
4007:
3991:
3988:
3981:
3977:
3973:
3965:
3962:
3959:
3955:
3949:
3945:
3941:
3936:
3932:
3922:
3908:
3886:
3882:
3859:
3855:
3832:
3828:
3817:
3787:
3778:
3763:
3759:
3756:
3753:
3747:
3744:
3723:
3719:
3715:
3710:
3706:
3696:
3680:
3677:
3674:
3669:
3665:
3661:
3656:
3652:
3644:
3640:
3636:
3631:
3627:
3621:
3617:
3610:
3607:
3594:
3581:
3576:
3573:
3568:
3560:
3556:
3552:
3547:
3544:
3541:
3534:
3530:
3526:
3521:
3514:
3510:
3506:
3501:
3494:
3490:
3486:
3480:
3475:
3470:
3467:
3462:
3454:
3450:
3446:
3439:
3434:
3431:
3428:
3424:
3419:
3414:
3411:
3403:
3398:
3396:
3392:
3383:
3379:
3366:
3361:
3357:
3353:
3350:
3345:
3341:
3337:
3332:
3328:
3324:
3319:
3315:
3311:
3306:
3302:
3296:
3291:
3288:
3285:
3281:
3277:
3274:
3254:
3240:
3238:
3234:
3229:
3216:
3209:
3205:
3199:
3195:
3189:
3182:
3178:
3172:
3168:
3156:
3143:
3135:
3131:
3127:
3122:
3117:
3113:
3090:
3086:
3077:
3072:
3059:
3054:
3051:
3046:
3043:
3023:
3018:
3015:
3010:
3007:
3002:
2999:
2989:
2984:
2982:
2977:
2964:
2956:
2952:
2948:
2943:
2939:
2931:
2927:
2921:
2917:
2910:
2907:
2898:
2883:
2880:
2875:
2867:
2863:
2859:
2854:
2851:
2848:
2841:
2837:
2833:
2828:
2821:
2817:
2813:
2808:
2801:
2797:
2793:
2787:
2782:
2777:
2774:
2769:
2761:
2757:
2753:
2746:
2741:
2738:
2735:
2731:
2726:
2721:
2718:
2710:
2705:
2689:
2685:
2676:
2672:
2662:
2649:
2642:
2638:
2634:
2627:
2622:
2619:
2616:
2612:
2608:
2605:
2600:
2596:
2590:
2585:
2582:
2579:
2575:
2571:
2568:
2560:
2550:
2535:
2531:
2527:
2524:
2521:
2516:
2512:
2508:
2503:
2499:
2495:
2492:
2484:
2474:
2472:
2462:
2453:
2451:
2447:
2443:
2433:
2431:
2427:
2423:
2413:
2411:
2406:
2393:
2388:
2385:
2380:
2372:
2368:
2364:
2359:
2356:
2353:
2346:
2342:
2338:
2333:
2326:
2322:
2318:
2313:
2306:
2302:
2298:
2292:
2287:
2282:
2279:
2274:
2266:
2262:
2258:
2251:
2246:
2243:
2240:
2236:
2231:
2226:
2223:
2215:
2210:
2208:
2204:
2200:
2195:
2185:
2168:
2165:
2161:
2138:
2135:
2131:
2121:
2107:
2101:
2097:
2093:
2088:
2084:
2080:
2075:
2071:
2066:
2062:
2058:
2052:
2048:
2044:
2039:
2035:
2031:
2026:
2022:
2017:
2013:
2009:
2003:
1999:
1995:
1990:
1986:
1982:
1977:
1973:
1968:
1964:
1961:
1952:
1936:
1932:
1909:
1905:
1882:
1878:
1855:
1851:
1828:
1824:
1801:
1797:
1774:
1770:
1747:
1743:
1720:
1716:
1705:
1701:
1688:
1683:
1679:
1675:
1672:
1667:
1663:
1659:
1654:
1650:
1646:
1641:
1637:
1633:
1628:
1624:
1618:
1613:
1610:
1607:
1603:
1599:
1596:
1588:
1583:
1581:
1577:
1568:
1555:
1547:
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1498:
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1471:
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827:
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549:
547:
544:
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537:
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532:
531:Joule heating
529:
527:
524:
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519:
517:
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475:
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454:
452:
449:
447:
446:Lorentz force
444:
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432:
429:
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417:
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365:
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352:
349:
347:
346:Magnetization
344:
342:
339:
337:
334:
332:
331:Magnetic flux
329:
327:
324:
322:
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314:
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269:
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244:
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239:
237:
236:Electric flux
234:
232:
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209:
207:
204:
202:
199:
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176:
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173:Computational
171:
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149:
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144:
140:
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136:
133:
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128:
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119:
115:
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108:
106:
105:voltage drops
101:
99:
95:
91:
86:
84:
79:
77:
72:
68:
66:
62:
58:
54:
50:
46:
39:
34:
30:
19:
5559:(in German).
5556:
5543:EDN magazine
5541:
5515:
5496:
5466:
5460:
5454:. Example 1.
5439:
5332:
5323:
5314:
5305:
5298:
5291:
5284:
5272:
5263:
5256:
5249:
5242:
5238:
5219:
5215:
5212:Applications
5045:
4873:
4660:
4657:
4518:
4413:
4307:
4254:
4194:
4178:
4170:
4151:Two or more
4150:
4142:
4024:
4013:
3923:
3818:
3780:The sign of
3779:
3697:
3595:
3399:
3389:
3380:
3246:
3232:
3230:
3157:
3074:To find the
3073:
2987:
2985:
2980:
2978:
2899:
2706:
2668:
2556:
2482:
2480:
2467:
2439:
2420:Two or more
2419:
2407:
2211:
2197:
2122:
1953:
1706:
1702:
1584:
1574:
1490:
1295:
1281:
1272:
1267:
1149:
1146:
1048:
1040:
974:
958:
949:
948:
691:Four-current
626:Linear motor
511:Electrolysis
391:Eddy current
351:Permeability
271:Polarization
266:Permittivity
116:
109:
102:
93:
89:
87:
80:
73:
69:
56:
52:
45:Two-terminal
43:
29:
5267:capillaries
5234:solid state
4016:capacitance
3243:Conductance
2675:reciprocals
2450:car battery
2426:logical AND
2207:reciprocals
2203:capacitance
1292:Conductance
954:daisy chain
661:Transformer
491:Capacitance
416:Faraday law
211:Coulomb law
153:Electricity
18:In Parallel
5497:Physiology
5420:References
5304:+ ... + 1/
5260:arterioles
5232:, then by
4157:logical OR
4020:capacitors
4014:The total
4010:Capacitors
3395:inductance
2671:resistance
2199:Capacitors
2192:See also:
2188:Capacitors
1954:Therefore
1580:inductance
728:Scientists
576:Waveguides
556:Resistance
526:Inductance
306:AmpĂšre law
5236:devices.
5090:≡
5077:∥
5064:∥
4981:≡
4973:−
4959:−
4938:−
4919:≡
4906:∥
4893:≡
4113:⋯
4044:∑
3946:∑
3675:−
3637:−
3574:−
3545:⋯
3468:−
3425:∑
3391:Inductors
3386:Inductors
3351:⋯
3282:∑
3237:arc lamps
2881:−
2852:⋯
2775:−
2732:∑
2613:∑
2576:∑
2559:Ohm's law
2525:⋯
2410:elastance
2386:−
2357:⋯
2280:−
2237:∑
1673:⋯
1604:∑
1576:Inductors
1571:Inductors
1469:−
1440:⋯
1363:−
1320:∑
1238:⋯
1169:∑
1101:∑
1064:∑
1014:⋯
884:Steinmetz
814:Kirchhoff
799:Jefimenko
794:Hopkinson
779:Helmholtz
774:Heaviside
636:Permeance
521:Impedance
261:Insulator
256:Gauss law
206:Conductor
183:Phenomena
178:Textbooks
158:Magnetism
5568:Category
5479:66-17612
5452:66-11527
5343:See also
5226:resistor
4870:Notation
4255:parallel
4153:switches
4147:Switches
3233:multiple
2430:AND gate
2422:switches
2416:Switches
909:Wiechert
864:Poynting
754:Einstein
601:DC motor
596:AC motor
431:Lenz law
216:Electret
65:resistor
61:topology
57:parallel
5440:Physics
4161:OR gate
3076:current
2553:Current
2477:Voltage
2442:battery
1045:Voltage
971:Current
894:Thomson
869:Ritchie
859:Poisson
844:Neumann
839:Maxwell
834:Lorentz
829:Liénard
759:Faraday
744:Coulomb
571:Voltage
546:Ohm law
168:History
76:voltage
5526:
5477:
5450:
5330:, and
5253:artery
4174:ampere
879:Singer
874:Savart
854:Ărsted
819:Larmor
809:Kelvin
764:Fizeau
734:AmpĂšre
656:Stator
163:Optics
53:series
5471:Wiley
5444:Wiley
5288:total
5279:aorta
5246:total
4195:From
4181:valve
2481:In a
961:point
904:Weber
899:Volta
889:Tesla
804:Joule
789:Hertz
784:Henry
769:Gauss
651:Rotor
5524:ISBN
5475:LCCN
5448:LCCN
5297:+ 1/
5290:= 1/
4441:and
4226:and
3874:and
2986:For
1924:and
1843:and
1789:and
824:Lenz
749:Davy
739:Biot
4253:in
4018:of
3698:If
1270:in
849:Ohm
55:or
5570::
5555:.
5540:.
5522:.
5518:.
5487:^
5446:.
5428:^
5321:,
5312:.
5283:1/
5262:+
5255:+
5248:=
4882:.
4163:.
3887:23
3860:13
3847:,
3833:12
3239:.
2983:.
2473:.
2440:A
2432:.
2153:=
2102:32
2089:31
2076:21
2053:23
2040:13
2027:12
2004:33
1991:22
1978:11
1951:.
1937:33
1910:22
1897:,
1883:11
1856:32
1829:31
1816:,
1802:21
1775:23
1762:,
1748:13
1735:,
1721:12
100:.
85:.
5546:.
5532:.
5481:.
5336:n
5333:R
5327:b
5324:R
5318:a
5315:R
5309:n
5306:R
5302:b
5299:R
5295:a
5292:R
5285:R
5264:R
5257:R
5250:R
5243:R
5197:.
5189:3
5185:R
5179:2
5175:R
5171:+
5166:3
5162:R
5156:1
5152:R
5148:+
5143:2
5139:R
5133:1
5129:R
5121:3
5117:R
5111:2
5107:R
5101:1
5097:R
5085:3
5081:R
5072:2
5068:R
5059:1
5055:R
5027:2
5023:R
5019:+
5014:1
5010:R
5002:2
4998:R
4992:1
4988:R
4976:1
4968:)
4962:1
4954:2
4950:R
4946:+
4941:1
4933:1
4929:R
4924:(
4914:2
4910:R
4901:1
4897:R
4890:R
4855:.
4847:3
4843:G
4837:2
4833:G
4829:+
4824:3
4820:G
4814:1
4810:G
4806:+
4801:2
4797:G
4791:1
4787:G
4779:3
4775:G
4769:2
4765:G
4759:1
4755:G
4748:=
4745:G
4725:.
4717:2
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4709:+
4704:1
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4692:2
4688:G
4682:1
4678:G
4671:=
4668:G
4644:.
4637:2
4633:G
4629:1
4624:+
4617:1
4613:G
4609:1
4604:=
4599:G
4596:1
4570:2
4566:G
4562:I
4557:+
4550:1
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4542:I
4537:=
4532:G
4529:I
4505:.
4500:2
4496:V
4492:+
4487:1
4483:V
4479:=
4476:V
4454:2
4450:G
4427:1
4423:G
4400:.
4395:2
4391:G
4387:+
4382:1
4378:G
4374:=
4371:G
4351:V
4346:2
4342:G
4338:+
4335:V
4330:1
4326:G
4322:=
4319:V
4316:G
4294:.
4289:2
4285:I
4281:+
4276:1
4272:I
4268:=
4265:I
4239:2
4235:G
4212:1
4208:G
4129:.
4124:n
4120:C
4116:+
4108:3
4104:C
4100:+
4095:2
4091:C
4087:+
4082:1
4078:C
4074:=
4069:i
4065:C
4059:n
4054:1
4051:=
4048:i
4040:=
4037:C
3992:t
3989:d
3982:j
3978:i
3974:d
3966:j
3963:,
3960:i
3956:L
3950:j
3942:=
3937:i
3933:v
3909:L
3883:M
3856:M
3829:M
3814:M
3810:L
3806:M
3802:M
3788:M
3764:2
3760:M
3757:+
3754:L
3748:=
3745:L
3724:2
3720:L
3716:=
3711:1
3707:L
3681:M
3678:2
3670:2
3666:L
3662:+
3657:1
3653:L
3645:2
3641:M
3632:2
3628:L
3622:1
3618:L
3611:=
3608:L
3598:M
3582:.
3577:1
3569:)
3561:n
3557:L
3553:1
3548:+
3542:+
3535:3
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3527:1
3522:+
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3507:1
3502:+
3495:1
3491:L
3487:1
3481:(
3476:=
3471:1
3463:)
3455:i
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3440:n
3435:1
3432:=
3429:i
3420:(
3415:=
3412:L
3367:.
3362:n
3358:G
3354:+
3346:3
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3338:+
3333:2
3329:G
3325:+
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3316:G
3312:=
3307:i
3303:G
3297:n
3292:1
3289:=
3286:i
3278:=
3275:G
3255:G
3217:.
3210:1
3206:R
3200:2
3196:R
3190:=
3183:2
3179:I
3173:1
3169:I
3144:.
3136:i
3132:R
3128:V
3123:=
3118:i
3114:I
3091:i
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3060:.
3055:N
3052:R
3047:=
3044:R
3024:.
3019:R
3016:1
3011:N
3008:=
3003:R
3000:1
2988:N
2965:.
2957:2
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2949:+
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2911:=
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2884:1
2876:)
2868:n
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2860:1
2855:+
2849:+
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2834:1
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2809:+
2802:1
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2794:1
2788:(
2783:=
2778:1
2770:)
2762:i
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2742:1
2739:=
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2727:(
2722:=
2719:R
2690:i
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2650:.
2643:i
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2623:1
2620:=
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2606:=
2601:i
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2591:n
2586:1
2583:=
2580:i
2572:=
2569:I
2536:n
2532:V
2528:=
2522:=
2517:2
2513:V
2509:=
2504:1
2500:V
2496:=
2493:V
2394:.
2389:1
2381:)
2373:n
2369:C
2365:1
2360:+
2354:+
2347:3
2343:C
2339:1
2334:+
2327:2
2323:C
2319:1
2314:+
2307:1
2303:C
2299:1
2293:(
2288:=
2283:1
2275:)
2267:i
2263:C
2259:1
2252:n
2247:1
2244:=
2241:i
2232:(
2227:=
2224:C
2169:i
2166:j
2162:M
2139:j
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2132:M
2108:)
2098:M
2094:+
2085:M
2081:+
2072:M
2067:(
2063:+
2059:)
2049:M
2045:+
2036:M
2032:+
2023:M
2018:(
2014:+
2010:)
2000:M
1996:+
1987:M
1983:+
1974:M
1969:(
1965:=
1962:L
1933:M
1906:M
1879:M
1852:M
1825:M
1798:M
1771:M
1744:M
1717:M
1689:.
1684:n
1680:L
1676:+
1668:3
1664:L
1660:+
1655:2
1651:L
1647:+
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1638:L
1634:=
1629:i
1625:L
1619:n
1614:1
1611:=
1608:i
1600:=
1597:L
1556:.
1548:2
1544:G
1540:+
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1523:2
1519:G
1513:1
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1502:=
1499:G
1477:.
1472:1
1464:)
1456:n
1452:G
1448:1
1443:+
1437:+
1430:3
1426:G
1422:1
1417:+
1410:2
1406:G
1402:1
1397:+
1390:1
1386:G
1382:1
1376:(
1371:=
1366:1
1358:)
1350:i
1346:G
1342:1
1335:n
1330:1
1327:=
1324:i
1315:(
1310:=
1307:G
1285:s
1282:R
1276:s
1273:R
1268:s
1254:.
1249:n
1245:R
1241:+
1233:3
1229:R
1225:+
1220:2
1216:R
1212:+
1207:1
1203:R
1199:=
1194:i
1190:R
1184:n
1179:1
1176:=
1173:i
1165:=
1162:R
1126:i
1122:R
1116:n
1111:1
1108:=
1105:i
1097:I
1094:=
1089:i
1085:V
1079:n
1074:1
1071:=
1068:i
1060:=
1057:V
1025:n
1021:I
1017:=
1011:=
1006:2
1002:I
998:=
993:1
989:I
985:=
982:I
938:e
931:t
924:v
20:)
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