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

Answer: (A)

5 s

Answer 2

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 ${{i}_{0}}$ .