Question 112: Electrostatics & Capacitance

Question

In the circuit shown, the energy stored in the capacitor is $n ~\mu \mathrm{J}$. The value of $n$ is __________

Accepted Answer

$
\begin{aligned}
& \mathrm{I}_1=\frac{12}{3+9}=1 \mathrm{~A} \\
& \mathrm{I}_2=\frac{12}{4+2}=2 \mathrm{~A}
\end{aligned}
$
$
\begin{aligned}
& \mathrm{V}_{\mathrm{A}}-\mathrm{V}_{\mathrm{C}}=3 \mathrm{I}_1=3 \mathrm{~V} \\
& \mathrm{~V}_{\mathrm{A}}-\mathrm{V}_{\mathrm{D}}=2 	imes 4=8 \mathrm{~V}
\end{aligned}
$
Subtracting eq. (1) from eq. (2)
$
\begin{aligned}
& \mathrm{V}_{\mathrm{C}}-\mathrm{V}_{\mathrm{D}}=5 \mathrm{~V} \Rightarrow \mathrm{V}=5 \mathrm{~V} \\
& \mathrm{U}=\frac{1}{2} \mathrm{CV}^2=\frac{1}{2} 	imes 6 	imes 5^2=75 \mu \mathrm{J}
\end{aligned}
$

Electrostatics & Capacitance

In the circuit shown, the energy stored in the capacitor is n ~\mu \mathrm{J}. The value of n is __________

Integer / Numeric Answer Type