First slide

Time -Varying current in L-R circuit

Question

An inductance L and a resistance R are first connected to a battery. After some time the battery is disconnected but L and R remain connected in a closed circuit. Then the current reduces to 37% of its initial value in time

Moderate

A

RL
B

$\frac{R}{L}$
C

$\frac{L}{R}$
D

$\frac{1}{L R}$

Solution

When battery disconnected current through the circuit start decreasing exponentially according to $i = i_{0} e^{- Rt / L}$ ̣
$\Rightarrow 0.37 i_{0} = i_{0} e^{- Rt / L} \Rightarrow 0.37 = \frac{1}{e} = e^{- Rt / L} \Rightarrow t = \frac{L}{R}$

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