First slide

Time -Varying current in L-R circuit

Question

A coil has an inductance of 2.5 H and a resistance of $0.5 Ω$ If the coil is suddenly connected across a 6.0 V battery then the time required for the current to rise 0.63 of its final value is

Moderate

A

3.5 s
B

4.0 s
C

4.5 s
D

5.0 s

Solution

$i = \frac{E}{R} (1 - e^{- Rt / L}) = I_{m} (1 - e^{- Rt / L}) When i = 0.63 I_{m} we get t = \frac{L}{R} = \frac{2.5}{0.5} = 5 s$

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