A coil of negligible resistance is connected in series with 90 resistor across 120 V, 60 Hz supply. A voltmeter reads 36 V across resistance. Inductance of the coil is

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Solution

Q.
A coil of negligible resistance is connected in series with 90 $Ω$ resistor across 120 V, 60 Hz supply. A voltmeter reads 36 V across resistance. Inductance of the coil is [2024]

1 0.76 H

2 0.286 H

3 2.86 H

4 0.91 H

Ans.
(1)

$36 = I_{r m s} R$

$36 = \frac{120}{\sqrt{X_{L}^{2} + R^{2}}} \times R$

$R = 90 Ω \Rightarrow 36 = \frac{120 \times 90}{\sqrt{X_{L}^{2} + 90^{2}}}$

$\sqrt{X_{L}^{2} + 90^{2}} = 300$

$X_{L}^{2} = 81900 \Rightarrow X_{L} = 286.18 Ω$

$ω L = 286.18$

$\Rightarrow L = \frac{286.18}{376.8} = 0.76 H$

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