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A series L-R circuit is connected to a battery of emf V. If the circuit is switched on at t = 0, then the time at which the energy stored in the inductor reaches (1/n) times of its maximum value, is:
- (L/R) ln((√n−1)/√n)
- (L/R) ln(√n/(√n−1))
- (L/R) ln(√n/(√n+1))
- (L/R) ln((√n+1)/(√n−1))
Correct answer: (L/R) ln(√n/(√n−1))
Solution
The correct option represents the time at which the energy stored in the inductor reaches a specific fraction of its maximum value, derived from the exponential growth of current in an L-R circuit. The formula captures the relationship between the inductance, resistance, and the logarithmic nature of energy storage in inductors.
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