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Question
A capacitance C, a resistance R and an emf ε are connected in series at t = 0. What is the maximum value of (a) the potential difference across the resistor (b) the current in the circuit (c) the potential difference across the capacitor (d) the energy stored in the capacitor (e) the power delivered by the battery and (f) the power converted into heat?
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Solution
(a) When the charge on the capacitor is zero, it acts as short circuit.
Thus, maximum value of potential difference across the resistor = ε (at t = 0)
(b) Maximum value of current in the circuit \[= \frac{\epsilon}{r}.........\left(\text{at }t = 0\right)\]
(c) Maximum value of potential difference across the capacitor = ε .............(at t = ∞, when the capacitor is fully charged and acts as a open circuit)
(d) Maximum energy stored in the capacitor \[= \frac{1}{2}C \epsilon^2.........\left(\text{at }t = \infty\right)\]
(e) Maximum power delivered by the battery \[= \frac{\epsilon^2}{r}\]
(f) Maximum power converted to heat \[= \frac{\epsilon^2}{r}\]
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