Question:
A parallel combination of two capacitors of capacities ' \(C\) ' and ' \(\frac{C}{3}\) ' respectively is connected across a battery of 12 volt. When both capacitors are fully charged, the charge and energy stored in them is \(Q_1, Q_2\) and \(E_1, E_2\) respectively. Then the ratio of \((E_1 - E_2)\) to \((Q_1 - Q_2)\) is
A parallel combination of two capacitors of capacities ' \(C\) ' and ' \(\frac{C}{3}\) ' respectively is connected across a battery of 12 volt. When both capacitors are fully charged, the charge and energy stored in them is \(Q_1, Q_2\) and \(E_1, E_2\) respectively. Then the ratio of \((E_1 - E_2)\) to \((Q_1 - Q_2)\) is
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Parallel capacitors:
Voltage same across each
Updated On: May 8, 2026
- 1 : 8
- 1 : 6
- 8 : 1
- 6 : 1
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The Correct Option is B
Solution and Explanation
Concept: \[ Q = CV \quad , \quad E = \frac{1}{2}CV^2 \]
Step 1: Charges. \[ Q_1 = 12C, \quad Q_2 = 4C \] \[ Q_1 - Q_2 = 8C \]
Step 2: Energies. \[ E_1 = \frac{1}{2}C(12)^2 = 72C \] \[ E_2 = \frac{1}{2}\frac{C}{3}(12)^2 = 24C \] \[ E_1 - E_2 = 48C \]
Step 3: Ratio. \[ \frac{E_1 - E_2}{Q_1 - Q_2} = \frac{48C}{8C} = 6 \] Final Answer: Option (B)
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