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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 10√2VThe 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 isXL−XC=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=10√2R amp. P.d. across L :IXL=IR=10√2V 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=10√2volts

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