JEE Mains · Physics · STD 12 - Electric potential and capacitance
- JEE Mains 2025
- Medium
- MCQ
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?
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(\mathrm{C}_2\gt\mathrm{C}_1, \mathrm{U}_2\gt\mathrm{U}_1\)
Step-by-step Solution
Detailed explanation
For a capacitor at steady state
\(q=C V \text { and } U=\frac{1}{2} C V^2\)
Since \(C_1\) and \(C_2\) are connected in parallel, \(V_1=V_2\).
Also from graph \(q_1 < q_2\)
\(\begin{aligned}
& \Rightarrow \quad C_1 V_1 < C_2 V_2 \\
& \text { i.e. } C_1 < C_2 \text { or } C_2>C_1 \\
& \qquad \frac{U_1}{U_2}=\frac{C_1 V_1^2}{C_2 V_2^2}=\frac{C_1}{C_2} < 1
\end{aligned}\)
or \(U_1 < U_2\) or \(U_2>U_1\)
\(q=C V \text { and } U=\frac{1}{2} C V^2\)
Since \(C_1\) and \(C_2\) are connected in parallel, \(V_1=V_2\).
Also from graph \(q_1 < q_2\)
\(\begin{aligned}
& \Rightarrow \quad C_1 V_1 < C_2 V_2 \\
& \text { i.e. } C_1 < C_2 \text { or } C_2>C_1 \\
& \qquad \frac{U_1}{U_2}=\frac{C_1 V_1^2}{C_2 V_2^2}=\frac{C_1}{C_2} < 1
\end{aligned}\)
or \(U_1 < U_2\) or \(U_2>U_1\)
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