The charge on capacitor of capacitance $15 \mu \mathrm{~F}$ in the figure given below is :

JEE Main · 2022 · 26 Jun 2022 · Shift 2 · Capacitance

The charge on capacitor of capacitance

15 μ F

in the figure given below is :

(A) $60 μ c$ ✓ Correct
(B) $130 μ c$
(C) $260 μ c$
(D) $585 μ c$

Answer: (A)

Solution

The three capacitors (10 μF, 15 μF, and 20 μF) are in series. The equivalent capacitance is

\frac{1}{C _{eq}} = \frac{1}{10} + \frac{1}{15} + \frac{1}{20} = \frac{12 + 8 + 6}{120} = \frac{26}{120}

, so

C_{eq} = \frac{60}{13} μ F

. The total charge is

Q = C_{eq} V = \frac{60}{13} \times 13 = 60 μ C

. In a series combination, the charge on each capacitor is the same, so the charge on the 15 μF capacitor is 60 μC.

JEE Main · 2022 · 26 Jun 2022 · Shift 2 · Single correct option

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