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A capacitor of capacitance C is allowed to discharge through a resistor R. Let t1 be the time required for the energy stored in the capacitor to become half of its initial value, and let t2 be the time required for the charge on it to fall to one-fourth of its initial value. What is the ratio t1/t2?

1. 1
2. 1/2
3. 1/4
4. 2

Correct answer: 1/4

Solution

The time constant for a capacitor discharging through a resistor is given by the exponential decay of charge and energy. The energy decreases to half its initial value in a time t1, while the charge decreases to one-fourth in a longer time t2, leading to the ratio t1/t2 being 1/4.

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