Two capacitors and are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are and , respectively. Which of the given statements is true? [2025] F

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Q.
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 [2025]

1 $C_{1} > C_{2}, U_{1} > U_{2}$

2 $C_{2} > C_{1}, U_{2} > U_{1}$

3 $C_{1} > C_{2}, U_{1} < U_{2}$

4 $C_{2} > C_{1}, U_{2} < U_{1}$

Ans.
(2)

For a capacitor at steady state

q = CV and $U = \frac{1}{2} C V^{2}$

Since $C_{1}$ and $C_{2}$ are connected in parallel, $V_{1} = V_{2}$

Also from graph $q_{1} < q_{2}$

$\Rightarrow C_{1} V_{1} < C_{2} V_{2}$

i.e., $C_{1} < C_{2}$ or $C_{2} > C_{1}$

$\frac{U_{1}}{U_{2}} = \frac{C_{1} V_{1}^{2}}{C_{2} V_{2}^{2}} = \frac{C_{1}}{C_{2}} < 1$

or $U_{1} < U_{2}$ or $U_{2} > U_{1}$

Solution

Q.
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 [2025]

1 $C_{1} > C_{2}, U_{1} > U_{2}$

2 $C_{2} > C_{1}, U_{2} > U_{1}$

3 $C_{1} > C_{2}, U_{1} < U_{2}$

4 $C_{2} > C_{1}, U_{2} < U_{1}$

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Solution

Q. Two capacitors C1 and C2 are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are U1 and U2, respectively. Which of the given statements is true [2025]

1 C1>C2, U1>U2

2 C2>C1, U2>U1

3 C1>C2, U1<U2

4 C2>C1, U2<U1

Ans. (2) For a capacitor at steady state q = CV and U=12CV2 Since C1 and C2 are connected in parallel, V1=V2 Also from graph q1<q2 ⇒ C1V1<C2V2 i.e., C1<C2 or C2>C1 U1U2=C1V12C2V22=C1C2<1 or U1<U2 or U2>U1

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Q.
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 [2025]

1 $C_{1} > C_{2}, U_{1} > U_{2}$

2 $C_{2} > C_{1}, U_{2} > U_{1}$

3 $C_{1} > C_{2}, U_{1} < U_{2}$

4 $C_{2} > C_{1}, U_{2} < U_{1}$