Peak Voltages in LCR Circuit – Rankers Physics
Topic: Alternating Current
Subtopic: LR, RC and LCR Circuits

Peak Voltages in LCR Circuit

Assertion (A): Peak voltage across the resistance can be greater than the peak voltage of the source in a series \(LCR\) circuit.
Reason (R): Peak voltage across the inductor can be greater than the peak voltage of the source in an series \(LCR\) circuit.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

Peak voltage across resistor is \(V_R = I_0 R\). Peak source voltage is \(V_0 = I_0 Z\). Since \(Z \ge R\), \(V_R \le V_0\). So A is false. Peak voltage across inductor is \(V_L = I_0 X_L\). At resonance, if \(X_L > R\), then \(V_L\) can be greater than \(V_0\) (voltage magnification). So R is true. Thus, A is false and R is true.

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