Question

Directions: Sketch the diagram for each item and solve what is being asked.

1. Three capacitors with individual capacitances of 2 μF, 5 μF, and 10 μF

respectively are connected in series with a 12V battery. What are the total

capacitance and total charge in the network?

2. Same capacitors in number 1 connected in a parallel. If the combined

charge in the network is 50 μC, what are the total voltage and total

capacitance in the network?

Answer 1

1.

$$\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}$$

$$\frac{1}{C_{eq}}=\frac{1}{2}+\frac{1}{5}+\frac{1}{10}=0.8$$

$$C_{eq}=1.25\:\rm \mu F$$

$$q=C_{eq}V\\ =1.25*10^{-6}*12=1.5*10^{-5}\: \rm C$$

2.

$$C_{eq}=C_1+C_2+C_3$$

$$C_{eq}=2+5+10=17\;\rm \mu F$$

$$V=q/C_{eq}\\ =50*10^{-6}/17*10^{-6}=2.9\: \rm V$$