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  4. If 110V D.C. is applied across a solenoid, a current of 1.1A is produced in it. When 110V A.C. is applied across the same coil, the current drops to 0.55A . If the frequency of the A.C. source is 50Hz , the inductance of the solenoid is

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Q. If $110V$ D.C. is applied across a solenoid, a current of $1.1A$ is produced in it. When $110V$ A.C. is applied across the same coil, the current drops to $0.55A$ . If the frequency of the A.C. source is $50Hz$ , the inductance of the solenoid is

NTA AbhyasNTA Abhyas 2020

Solution:

$R=\frac{110}{1 . 1}=100\Omega$
Impedance, $Z=\frac{110}{0 . 55}=200\Omega$
$L^{2}\omega ^{2}=Z^{2}-R^{2}$ or $L\omega =\sqrt{200^{2} - 100^{2}}$