In the circuit shown, the energy stored in the capacitor is . The value of is _______. [2023]

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Solution

Q.
In the circuit shown, the energy stored in the capacitor is $n μ J$ . The value of $n$ is _______. [2023]

Ans.
(75)

$I_{1} = \frac{12}{3 + 9} = 1 A$

$I_{2} = \frac{12}{4 + 2} = 2 A$

$V_{A} - V_{C} = 3 I_{1} = 3 V$ ...(i)

$V_{A} - V_{D} = 2 \times 4 = 8 V$ ...(ii)

Subtracting eq. (i) from eq. (ii),

$V_{C} - V_{D} = 5 V \Rightarrow V = 5 V$

$U = \frac{1}{2} C V^{2} = \frac{1}{2} \times 6 \times 5^{2} = 75 μ J$

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