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Question

In a series L-C-R circuit, voltage across resistor, capacitor and inductor is 20V each. If capacitor is short circuited the voltage across inductor is?

A
102V
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B
52V
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C
202V
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D
52V
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Solution

The correct option is A 102V
The voltage across Inductor lags behind the current through the resistor. The voltage across the capacitor leads the current through R.

WhenVR=VL=VC = potentials across resistor, inductor and capacitors are all equal, thenI×XL=I×XC, and they are in opposite phase. So they cancel. The collective impedance isXLXC=0 The net voltage across the 3 elements is only 10V. So the voltage applied across these elements, is 10V.

Now if the capacitance is shorted, only inductor and resistor are there in the circuit. SoZ=[R2+X2l]=2R There is an external voltage source of 10V.
So current I=102R amp.
P.d. across L :IXL=IR=102V
or,

The voltages across Resistance and voltage across inductor have a phase difference of 90 deg. Hence, the net voltage =V2L+V2R=10V
=>2VR=10V
=>VR=VL=102volts

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