A capacitor with a capacitance of 100 is charged to a potential...

A capacitor with a capacitance of

100 \mu\text{F}

is charged to a potential difference of

24 \text{ V}

. After disconnecting the charging battery, the capacitor is connected to a different battery of emf

12 \text{ V}

such that the positive plate of the capacitor is attached to the positive terminal of the battery. Determine the amount of charge that flows through the

12 \text{ V}

battery.

Options

A $1200 \mu\text{C}$
B $2400 \mu\text{C}$
C $3600 \mu\text{C}$
D $600 \mu\text{C}$

Correct answer

A. $1200 \mu\text{C}$

Step-by-step solution

Initial charge on the capacitor is

q_i = C V_i

q_i = 100 \mu\text{F} \times 24 \text{ V} = 2400 \mu\text{C}

When connected to the

12 \text{ V}

battery with matching polarities, the final potential difference across the capacitor becomes

V_f = 12 \text{ V}

.

Final charge on the capacitor is

q_f = C V_f

q_f = 100 \mu\text{F} \times 12 \text{ V} = 1200 \mu\text{C}

The amount of charge that flows through the battery is

\Delta q = |q_f - q_i|

\Delta q = |1200 \mu\text{C} - 2400 \mu\text{C}| = 1200 \mu\text{C}

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