Physics 212 and 222
Parallel and Series Circuits
Series and Parallel
Resistors in Series
Resistors in Parallel
Capacitors in Series
Capacitors in Parallel
Inductors in Combination
1
Physics 212 and 222
Parallel 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.
2
Circuits will often have elements in combination of series and
parallel sets.
1
Physics 212 and 222
Parallel and Series Circuits
V
+
-
R1
Resistors in series add
together to form an
equivalent
q
resistance.
For resistors in series, the
currents are the same.
Req
2
For resistors in series,
voltages add.
Req = R1 + R2
I eq = I1 = I 2
3
Veq = V1 + V2
Physics 212 and 222
Parallel and Series Circuits
•V
•+
••R1
•The inverse of resistors in
parallel add together to
form the inverse of an
equivalent resistance.
•For resistors in parallel,
the currents add.
•Req
2
1
1
1
= +
Req R1 R2
•For resistors in parallel,
voltages are the same.
I eq = I1 + I 2
4
Veq = V1 = V2
2
Physics 212 and 222
Parallel and Series Circuits
V
-
+
C1
C2
The inverse of capacitors
in series add together to
form the inverse an
equivalent capacitance.
For capacitors in series,
the voltages add.
Ceq
For capacitors in series,
charge stays the same.
1
1
1
=
+
Ceq C1 C2
Veq = V1 + V2
5
Qeq = Q1 = Q2
Physics 212 and 222
Parallel and Series Circuits
V
+
C1
CCeq
2
Capacitors in parallel add
together to form an
equivalent
q
capacitance.
p
For capacitors in parallel,
the voltages stay the same.
For capacitors in parallel,
charges add.
Ceq = C1 + C2
Veq = V1 = V2
6
Qeq = Q1 + Q2
3
Physics 212 and 222
Parallel and Series Circuits
Inductors behave like resistors when put in combination
except that one inductor can mutually interact with another
M = k
L1 L2
Series
Leq = L1 + L2 ± 2M
Parallel
7
1
1
1
=
+
Leq L1 ± M L2 ± M
Physics 212 and 222
Parallel and Series Circuits
Series and Parallel
Resistors in Series
Resistors in Parallel
Capacitors in Series
Capacitors in Parallel
Inductors in Combination
8
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