Question

A coil of $40\, H$ inductance is connected in series with a resistance of $ 8\,\Omega $ and the combination is joined to the terminals of a $2 \,V$ battery. The time constant of the circuit is

• A. 5 s
• B. $ \frac{1}{5}s $
• C. 40 s
• D. 20 s

Answer 1

The Correct Option is A

Time constant of L-R circuit is, $ \tau =\frac{L}{R} $ Here, $ L=40\,H,R=8\,\Omega ,E=2V $ $ \therefore $ $ \tau =\frac{40}{8}=5s $ At a time equal to one time constant the current has risen to $ \left( 1-\frac{1}{e} \right) $ or about $63\%$ of its initial value $ {{i}_{0}} $ .