Answer to Question #319404 in Physics for Nasi

Question

1. Using the definition C = Q/V, show that for a SERIES connection of capacitors:

1/C1/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 = QV, 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

1. For series connection

$$Q_1=Q_2=Q,\quad V_1+V_2=V$$

Hence

$$V=V_1+V_2=\frac{Q_1}{C_1}+\frac{Q_1}{C_1}=\frac{Q}{C}$$

Finally

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

2. For parallel connection

$$Q_1+Q_2=Q,\quad V_1=V_2=V$$

Hence

$$C_1V_1+C_2V_2=CV$$

Finally

$$C_1+C_2=C$$