Question

Two capacitors $C_{1}=4 \,\mu F$ and $C_{2}=4\, \mu F$ in series, are connected in parallel to a third capacitor $C _{3}=4 \,\mu F$. This arrangement is then connected to a battery of e.m.f. $=4 \,V$, as shown in the figure. How much energy is given by the battery in charging the capacitors?

• A. $96 \times 10^{-6} J$
• B. $48 \times 10^{-6} J$
• C. $\left(\frac{32}{3}\right) \times 10^{-6} J$
• D. $\left(\frac{16}{3}\right) \times 10^{-6} J$

Answer 1

Answer: (A)

$C_{\text {eq }}=2+4=6\, \mu F$
$U_{\text {cap }}=\frac{1}{2} C_{\text {eq }} V^{2}=\frac{1}{2} \cdot(6 \mu) \cdot(4)^{2}=48\, \mu J$
$U_{\text {Battery }}=2 U_{\text {cap }}=96 \,\mu J$