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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- 1 : 8
- 1 : 6
- 8 : 1
- 6 : 1
The Correct Option is B
Solution and Explanation
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A circuit consisting of a capacitor C, a resistor of resistance R and an ideal battery of emf V, as shown in figure is known as RC series circuit.
As soon as the circuit is completed by closing key S₁ (keeping S₂ open) charges begin to flow between the capacitor plates and the battery terminals. The charge on the capacitor increases and consequently the potential difference Vc (= q/C) across the capacitor also increases with time. When this potential difference equals the potential difference across the battery, the capacitor is fully charged (Q = VC). During this process of charging, the charge q on the capacitor changes with time t as
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