Question

In a LR circuit of $3mH$ inductane and $4\Omega$ resistance, emf $E=4cos\left(1000t\right)$ volt is applied. The amplitude of current is:

• A. $0.8A$
• B. $\frac{4}{7}A$
• C. $1.0A$
• D. $\frac{4}{\sqrt{7}}A$

Answer 1

The correct option is A $0.8A$

Given : $L=3mH=3\times {10}^{-3}H$ $R=4\Omega$

Emf $E=4cos1000t$

$\therefore$ $E_o=4$ volt and $\omega =1000$

Inductive reactance $X_L=\omega L=1000\times 3\times {10}^{-3}=3\Omega$

Impedance $Z=\sqrt{R^2+X_L^2}=\sqrt{4^2+3^2}=5\Omega$

Current amplitude $I=\frac{E_o}{Z}=\frac{4}{5}=0.8A$