JEE Mains · Physics · STD 12 - 2. Electric potential and 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 \(\mathrm{C}_2\gt\mathrm{C}_1, \mathrm{U}_2 \lt \mathrm{U}_1\)
- B \(\mathrm{C}_1\gt\mathrm{C}_2, \mathrm{U}_1\gt\mathrm{U}_2\)
- C \(\mathrm{C}_1\gt\mathrm{C}_2, \mathrm{U}_1 \lt \mathrm{U}_2\)
- D \(\mathrm{C}_2\gt\mathrm{C}_1, \mathrm{U}_2\gt\mathrm{U}_1\)
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 \(q_1 C_1 \\ & \qquad \frac{U_1}{U_2}=\frac{C_1 V_1^2}{C_2 V_2^2}=\frac{C_1}{C_2} U_1\)
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