Question

In an a.c circuit, the resistance $R=0.2\Omega$. At a certain instant $V_A-V_B=0.5\text{V},i=0.5\text{A}$ and the current $i$ is increasing at the rate of $\frac{\Delta i}{\Delta t}=8{\text{As}}^{-1}$. The inductance of the coil is

• A. $0.02\text{H}$
• B. $0.01\text{H}$
• C. $0.5\text{H}$
• D. $0.05\text{H}$

Answer 1

The correct option is D $0.05\text{H}$


From $\text{KVL}$ ,

$V_A-V_B=L\frac{di}{dt}+iR$

Substituting the data given in the question,

$0.5=(L\times 8)+0.5\times 0.2$

$\Rightarrow 0.5-0.1=8L$

$\Rightarrow L=\frac{0.4}{8}=5\times {10}^{-2}=0.05\text{H}$

Hence, option (d) is the correct answer.