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There is a inductor connected with voltage 10V. AC volt 50Hz such that the current flowing in the inductor is 0.1A. The phase angle between current and voltage is 60°. Find impedance, resistance, and inductance of conductor.
Asked by sharmujjwal00 | 17 Oct, 2019, 06:59: AM
current passing through inductor,  im = V / (R2 + L2ω2 )1/2 .............. (1)
where V is applied voltage, R is resistance of inductor, L is inductance and ω = 2πf , where f is frequency of AC voltage.

If the current is 0.1 A and applied voltage is 10 V, then we have,   0.1 = 10/ (R2 + L2ω2 )1/2 ..............(2)

Impedence = (R2 + L2ω2 )1/2 = 100 Ω

From eqn.(2), we get,  (R2 + L2ω2 ) = 10000 ..............(3)

Phase angle φ is given by, tan φ = Lω/R ............(4)

if phase angle is 60°, then we have tan 60° = ( Lω / R ) = √3   ,  i.e,  Lω = √3 R  ...............(4)

using eqn.(4), we rewrite eqn.(3) as ,  R2 + 3 R2 = 4 R2 = 10000   i.e.  R = 50 Ω

Inductance is obtained from eqn. (4) as , L = √3 R / ω = ( √3 × 50 ) /(2π×50) = 0.276 H
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