Question

A current 4 A flows in a coil when connected to a 12 V dc source. If the same coil is connected to a 12 V ac source $(\omega =50rad{s}^{-1})$ a current of 2.4 A flows in the circuit. The inductance of the coil is

• A. 80 mΩ
• B. 90 mΩ
• C. 60 mΩ
• D. 72 mΩ

Answer 1

The correct option is A

80 mΩ

$Z=\sqrt{R^2+{\omega }^2{L}^2}andi=\frac{V}{Z}\Rightarrow i=\frac{V}{\sqrt{R^2+{\omega }^2{L}^2}}Whendcisappliedi=\frac{V}{R}[\therefore \omega =0]i.e.,R=\frac{12}{4}=3\Omega whenacisappliedZ=\frac{V}{1}=\frac{12}{2.4}=5\Omega R^2+{\omega }^2{L}^2=Z^2\Rightarrow 3^2+\left({50}^2\right)L^2=5^2\Rightarrow L=0.08\Omega =80m\Omega$