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Question

A resistor, an inductor, and a capacitor are connected in series with a 120 V,100 Hz ac source. Voltage leads the current by 35 in the circuit. If the resistance of the resistor is 10Ω and the sum of inductive and capacitive reactance is 17Ω, calculate self-inductance of the inductor.

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Solution

Given:-
phase difference ϕ=35°,R=10Ω

Sum of reactance of inductor and capacitor (XL+XC)=17eqn(1)

Frequency of applied voltage, f=100Hz

So, angular frequency=2π×100

Now, for LCR circuit, we know

tanϕ=XLXCR

or XLXC=Rtanϕ=10tan35°

XL+XC=17 [Using eq.1]

2XL=17+(10×0.7)

XL=12

ωL=12

L=122π100=1.9×102H

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