In the given figure, the charge stored in $6 \mu \mathrm{~F}$ capacitor, when points A and B are joined by a connecting wire is ______ $\mu \mathrm{C}$.

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Capacitance

In the given figure, the charge stored in

6 μ F

capacitor, when points A and B are joined by a connecting wire is ______

μ C

Answer: 36

Solution

Joining A and B with a wire places them at the same potential. At steady state, no current flows through a capacitor branch, so current flows only along the resistor path: from the 9 V terminal through the 6 Ω resistor to node A(=B), then through the 3 Ω resistor to ground.

R_{e q} = 6 + 3 = 9 Ω, i = \frac{9}{9} = 1 A

The drop across the 6 Ω resistor is

1 \times 6 = 6

V, so node A (and hence B) sits at

9 - 6 = 3

V above ground.

The 6 μF capacitor connects the 9 V terminal to node B, so the voltage across it is

9 - 3 = 6

Q = C V = 6 μ F \times 6 V = 36 μ C

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Integer answer

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