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. ​

Question

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

(1) 0.76 H 

(2) 2.86 H 

(3) 0.286 H 

(4) 0.91 H

Answer 1

Correct option is :  (1) 0.76 H 

\(36=\mathrm{I}_{\mathrm{rms}} \mathrm\ {R}\)

\(36=\frac{120}{\sqrt{\mathrm{X}_{\mathrm{L}}^{2}+\mathrm{R}^{2}}} \times \mathrm{R}\)

\(\mathrm{R}=90 \ \Omega \Rightarrow 36=\frac{120 \times 90}{\sqrt{\mathrm{X}_{\mathrm{L}}^{2}+90^{2}}}\)

\(\sqrt{\mathrm{X}_{\mathrm{L}}^{2}+90^{2}}=300\)

\(\mathrm{X}_{\mathrm{L}}^{2}=81900\)

\(\mathrm{X}_{\mathrm{L}}=286.18\)

\(\omega \mathrm{L}=286.18\)

\(\mathrm{L}=\frac{286.18}{376.8}\)

\(\mathrm{L}=0.76 \mathrm{H}\)