Introductory Physics Volume Two

64 Circuits 3.7
Theorem: Effective Resistance
Series R = R 1 + R 2
Parallel
1
R = 1 + 1 R 1 R 2
§ 3.7 Capacitors in Combination
Capacitors in series and parallel can also be treated as a single
capacitor. The argument is much the same, but with charge rather
than current.
Suppose that you have two capacitors in series. Then the charges
on each must be the same.
Q 1 = Q 2 = Q
While the potential drop across the pair is the sum of the potential
drop across each
∆V = ∆V 1 + ∆V 2
+
–
−→
Series Capacitors
= Q 1
+ Q 2
= Q + Q C 1 C 2 C 1 C 2
1
C = ∆V
Q = 1 + 1 C 1 C 2
+
Parallel Capacitors
+Q
ΔV 1
-Q –
+Q 1 +Q 2
ΔV
+Q +
-Q
ΔV 1
-Q 2
2
-Q
For capacitors in parallel the potential is the same.
–
∆V 1 = ∆V 2 = ∆V
While the net charge that flows into the system is shared between the
capacitors.
Q = Q 1 + Q 2
= C 1 ∆V 1 + C 2 ∆V 2 = C 1 ∆V + C 2 ∆V
−→ C =
Q
∆V = C 1 + C 2