Determine the charge on the capacitor in the following circuit: (a) 200μC (b) 2μC (c) 10μC (d) 60μC

Answer: (a). Steady state: capacitor branch open. 2+10 = 12 Ω in parallel with 4 Ω gives 3 Ω; total 6+3 = 9 Ω. I = 72/9 = 8 A; voltage across the parallel part = 8×3 = 24 V. Current in 2 Ω + 10 Ω: 24/12 = 2 A, so V₁₀ = 20 V (capacitor is across it). Q = 10×20 = 200, so the answer is (a) 200.

Determine the charge on the capacitor in the following circuit: | JEE Main 2019 (9 Apr, Shift 1)

Q36JEE Main 2019 · 9 APR · SHIFT 1Medium

Capacitors in DC Circuits & RC

Determine the charge on the capacitor in the following circuit:

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Answer: (a)

Steady state: capacitor branch open. $2+10 = 12\ \Omega$ in parallel with $4\ \Omega$ gives $3\ \Omega$ ; total $6+3 = 9\ \Omega$ .
$I = \dfrac{72}{9} = 8\text{ A}$ ; voltage across the parallel part $= 8\times3 = 24\text{ V}$ .
Current in $2\ \Omega + 10\ \Omega$ : $\dfrac{24}{12} = 2\text{ A}$ , so $V_{10} = 20\text{ V}$ (capacitor is across it).
$Q = 10\times20 = 200\ \mu\text{C}$ , so the answer is (a) $200\ \mu\text{C}$ .

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