A capacitor $\mathrm{C}_{1}$ of capacitance $5 \mu \mathrm{~F}$ is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor $\mathrm{C}_{2}$ of capacitance $10 \mu \mathrm{~F}$ as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor $\mathrm{C}_{2}$ is ______ $\mu \mathrm{C}$.

JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Capacitance

A capacitor

C_{1}

of capacitance

5 μ F

is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor

C_{2}

of capacitance

10 μ F

as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor

C_{2}

is ______

μ C

Answer: 100

Solution

Initially, the charge on

C_{1}

Q = C_{1} V_{0} = 5 \times 30 = 150 μ C

. When the switch is closed, charge redistributes until both capacitors reach the same potential. By charge conservation, the common potential is

V = \frac{Q}{C _{1} + C _{2}} = \frac{150}{15} = 10 V

. The charge on

C_{2}

Q_{2} = C_{2} V = 10 \times 10 = 100 μ C

JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Integer answer

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