Question

When a coil is connected to a D.C. source of e.m.f. 12 volt, then a current of 4 ampere flows in it. If the same coil is connected to a 12 volt, 25 cycle/s A.C sources, then the current flowing in it is 2.4 A. The self-inductance of the coil will be ______

Options

• 48 H

• 4 H

• 0.16 H

• 8 x 10^-2 H

Answer 1

When a coil is connected to a D.C. source of e.m.f. 12 volt, then a current of 4 ampere flows in it. If the same coil is connected to a 12 volt, 25 cycle/s A.C sources, then the current flowing in it is 2.4 A. The self-inductance of the coil will be 0.16 H.

Explanation:

R = ${\displaystyle \frac{\text{V}}{\text{I}}=\frac{12}{4}=3\Omega }$

∴ Z = ${\displaystyle \frac{{\text{e}}_{\text{rms}}}{{\text{i}}_{\text{rms}}}=\frac{12}{2.4}=5}$

Z² = R² + ${\displaystyle {\text{X}}_{\text{L}}^2}$

∴ ${\displaystyle {\text{X}}_{\text{L}}^2}$ = 25 - 9 = 16

∴ ${\displaystyle {\text{X}}_{\text{L}}=\omega \text{L}=4}$

∴ L = ${\displaystyle \frac{4}{25}=0.16}$ H