in a series R-L-C circuit at resonance, the voltages across the resistor and the...
Question
in a series R-L-C circuit at resonance, the voltages across the resistor and the inductor are 30V and 40V respectively, what is the voltage across the capacitor?Options
A) 30V
B) 40V
C) 50V
D) 70V
Related Lesson: Impedance | Electromagnetic Induction and AC Circuits
The correct answer is B.
Explanation:
At resonance, inductive reactant XL is equal to the capacitive reactance XC
i.e. XL = XC
and XL = VL/IL
and XC = VC/IC
i.e. XL = XC
and XL = VL/IL
and XC = VC/IC
Again since the components are in series, the same current flows in the series arrangment
i.e. IL = IC
at resonance, VL/IL = VC/IC
∴ VL = VC
= 40V
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At resonance, inductive reactant XL is equal to the capacitive reactance XC
i.e. XL = XC
and XL = VL/IL
and XC = VC/IC
Again since the components are in series, the same current flows in the series arrangment
i.e. IL = IC
at resonance, VL/IL = VC/IC
∴ VL = VC
= 40V