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Question

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

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Solution

Let a LCR circuit is connected across an AC supply with the emf E = E0 sin ωt.
Let the inductance in the circuit be L
Let the net impedence of the circuit be Z=R2+(XL-XC)2
Where,
R = resistance in the circuit
XL = reactance due to inductor
XC = reactance due to capacitor
The magnitude of the voltage across the inductor is given by
V=Ldidt
The current in the circuit can be written as I=I0sin(ωt+ϕ)
Where, Ï• is the phase difference between the current and the supply voltage
Thus, the voltage across the inductor can be written as
V=LI0cos(ωt+ϕ)
Thus peak value of the voltage across the inductor is given by
V=LI0V=E0Z×L
Therefore, the peak voltage across the inductor is given by V=E0Z×L
At resonance Z = R,
V=E0R×L,
If LR>1
V > E0
Therefore if magnitude of LR>1 at resonance the value of the voltage across the inductor will bw greater than the peak value of the supply voltage.

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