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 = `"V"/"I" = 12/4 = 3 Omega`

∴ Z = `"e"_"rms"/"i"_"rms" = 12/2.4 = 5`

Z² = R² + `"X"_"L"^2`

∴ `"X"_"L"^2` = 25 - 9 = 16

∴ `"X"_"L" = omega"L" = 4`

∴ L = `4/25 = 0.16` H