Answer to Question #304851 in Electric Circuits for Kim

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

Explanations & Calculations

1)

• If the total capacitance is C,

$\qquad\qquad \begin{aligned} \small \frac{1}{C}&=\small \frac{1}{2}+\frac{1}{5}+\frac{1}{10}\\ \small C&=\small \frac{4}{5}=0.8\,\mu F(\text{less than the lowest one}) \end{aligned}$

• Apply Q =CV

$\qquad\qquad \begin{aligned} \small Q&=\small 0.8\,\mu F\times12\,V=9.6\,\mu C \end{aligned}$

2)

• The sum of charge on each capacitor is equal to 50. Then

$\qquad\qquad \begin{aligned} \small q_1+q_2+q_3&=\small 50\,\mu C\\ \small V(2\mu F+5\mu F+10\mu F)&=\small 50\,\mu C\\ \small V&=\small 2.9\,V \end{aligned}$

• If the total capacitance is C,

$\qquad\qquad \begin{aligned} \small C&=\small 2+5+10\\ &=\small 17\,\mu F \end{aligned}$