Question

An inductive coil has a resistance of $100\Omega$. When an a.c. signal of frequency $1000Hz$ is fed to the coil, the applied voltage leads the current by ${45}^o$. What is the inductance of the coil?

• A. $10mH$
• B. $12mH$
• C. $16mH$
• D. $20mH$

Answer 1

The correct option is C $16mH$

The applied voltage leads the current by ${45}^o$
i.e., $\frac{X_L}{R}=\tan {45}^o$
$X_L=R$
$\Rightarrow 2\times 3.14\times 1000L=100$
$\Rightarrow 6280L=100$
$\Rightarrow L=\frac{25}{1570}=0.01592\cong 16mH$