Question

1. Using the definition C=Q/V, show that for a SERIES connection of capacitors: 1/C = 1/C1 + 1/C2. What does this equation mean? What happens to C as more and more capacitors are connected in series?
2. Using the definition C=Q/V, show that for a PARALLEL connection of capacitors: C= C1+C2. What does this equation mean? What happens to C as more and more capacitors are connected in parallel?

Answer 1

Gives

(a) series combination

First capacitor capacitance =c₁

Second capacitor capacitance=c₂

V=V₁+V₂

$\frac{Q}{C}=\frac{Q}{C_1}+\frac{Q}{C_2}$

$\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}$

$C<C_1,C<C_2$

(b)

Parrelled combination

Q=Q₁+Q₂

$CV=C_1V+C_2V$

$C=C_1+C_2$

$C>C_1 ,C>C_2$