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In the circuit shown, the energy stored in the capacitor is n μJ. The value of n is ______. [Figure: a diamond bridge with top, bottom, left and right vertices. 3 Ω from top to left, 4 Ω from top to right, 9 Ω from left to bottom, 2 Ω from right to bottom. A 12 V cell is connected between the top vertex and the bottom vertex. A 6 μF capacitor joins the left and right vertices.]

Asked in JEE Main 13th April 2nd Shift 2023 · Capacitors in DC circuits

Figure: Capacitors in DC circuits
Answer: 75

Step-by-step solution

Steady state: no current in the capacitor, each side is a divider across 12 V.

Left vertex (bottom = 0): 12×9/(3+9)=9 V.

Right vertex: 12×2/(4+2)=4 V.

Capacitor voltage =5 V.

U=1/2×6×5²=75 μJ, so n=75.

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