Question

A coil of inductance $300\text{mH}$ and resistance $2$ $\Omega$ is connected to a source of voltage $2\text{V}$. The current reaches half of its steady state value in

Take $\ln 2=0.693$

• A. $0.15\text{s}$
• B. $0.3\text{s}$
• C. $0.05\text{s}$
• D. $0.1\text{s}$

Answer 1

The correct option is D $0.1\text{s}$

During growth of current in the coil,

$i=i_0(1-e^{-Rt/L})$

For $i=\frac{i_0}{2}$,

$\frac{i_0}{2}=i_0(1-e^{-Rt/L})$

$\Rightarrow t=\frac{L}{R}\ln 2$

$=\frac{300\times {10}^{-3}}{2}\times 0.693=0.1\text{s}$