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1

Physics 212 and 222Parallel and Series Circuits

Series and Parallel

Resistors in Series

Resistors in Parallel

Capacitors in Series

Capacitors in Parallel

Inductors in Combination

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2

Physics 212 and 222Parallel and Series Circuits

A circuit element is in series with another circuit element if at least one side of the element is attached to a side of the another element and nothing else.

A circuit element is in parallel with another circuit element if both sides of the element are attached to separate sides of another element and at least one other thing.

Circuits will often have elements in combination of series and parallel sets.

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Physics 212 and 222Parallel and Series Circuits

R2

-+

V

R1

Resistors in series add together to form an equivalent resistance.

For resistors in series, the currents are the same.

For resistors in series, voltages add.

21 RRReq

21 VVVeq 21 IIIeq

Req

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Physics 212 and 222Parallel and Series Circuits

•The inverse of resistors in parallel add together to form the inverse of an equivalent resistance.

•For resistors in parallel, the currents add.

•For resistors in parallel, voltages are the same.

21 VVVeq 21 IIIeq

•R2

•-•+

•V

•R1

•Req

21

111

RRReq

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5

Physics 212 and 222Parallel and Series Circuits

The inverse of capacitors in series add together to form the inverse an equivalent capacitance.

For capacitors in series, the voltages add.

For capacitors in series, charge stays the same.

21

111

CCCeq

21 QQQeq 21 VVVeq

-+

V

C1

C2

Ceq

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6

Physics 212 and 222Parallel and Series Circuits

Capacitors in parallel add together to form an equivalent capacitance.

For capacitors in parallel, the voltages stay the same.

For capacitors in parallel, charges add.

21 CCCeq

21 QQQeq 21 VVVeq

-+

V

C1

C2Ceq

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Physics 212 and 222Parallel and Series Circuits

Inductors behave like resistors when put in combinationexcept that one inductor can mutually interact with another

1 2 2eqL L L M

1 2 M k L L

1 2

1 1 1

eqL L M L M

Series

Parallel

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8

Physics 212 and 222Parallel and Series Circuits

Series and Parallel

Resistors in Series

Resistors in Parallel

Capacitors in Series

Capacitors in Parallel

Inductors in Combination