JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Capacitance

Two capacitors

C_{1}

and

C_{2}

are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are

U_{1}

and

U_{2}

, respectively. Which of the given statements is true ?

(A) $C_{1} > C_{2}, U_{1} > U_{2}$
(B) $C_{2} > C_{1}, U_{2} < U_{1}$
(C) $C_{1} > C_{2}, U_{1} < U_{2}$
(D) $C_{2} > C_{1}, U_{2} > U_{1}$ ✓ Correct

Answer: (D)

Solution

Since

C_{1}

and

C_{2}

are connected in parallel to the same battery, both charge to the same final potential difference V. From the charge-time graph, capacitor 2 reaches a higher steady charge (

q_{2} > q_{1}

) at this same V, which by

q = C V

means

C_{2} > C_{1}

The energy stored in a capacitor is

U = \frac{1}{2} C V^{2}

; since both share the same V,

U_{2} = \frac{1}{2} C_{2} V^{2} > \frac{1}{2} C_{1} V^{2} = U_{1}

C_{2} > C_{1}

and

U_{2} > U_{1}

JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Single correct option

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JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Capacitance

Solution

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