Can the peak voltage across the inductor be greater than the peak voltage of the source in an LCR circuit?

Yes.

Let the LCR circuit be connected across an AC supply of voltage … (i)


Now, the impedance in an AC circuit is given by


…. (ii)


where R = resistance, XL = inductive reactance,


Xc = capacitive reactance,


ω = angular frequency of oscillation of current,


L = inductance,


C = capacitance


Hence, the current in the circuit is given by … (iii),


where V = voltage,


Z = impedance


… (iv)


Now, at resonance, --------------(v)


Substituting (v) in (iv), we get


Current at resonance : … (vi)


Hence, at resonance, voltage across the inductor


… (vii)


where Ires = current at resonance, XL = inductive reactance, V = source voltage = V0sinωt, where V0 = peak voltage, ω = angular frequency, t = time, R = resistance, L = inductance


Since ω = angular frequency is always greater than equal to 1,


Therefore, voltage across the inductor VL will be greater than the source voltage V if > 1. (Ans)


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