Assertion: In a series LCR circuit, if the rms voltages across the inductor, capacitor, and resistor are 60 V , 20 V , and 30 V respectively, the peak voltage of the AC source is 50 2 V . Reason: The voltages across the inductor and capacitor are out of phase by radians, and their resultant is out of phase with the resistor's voltage by /2 radians.

Step-by-step solution

Assertion: The rms voltage of the source is found using phasor addition: V_ rms = V_R^2 + (V_L - V_C)^2 V_ rms = 30^2 + (60 - 20)^2 = 900 + 1600 = 50 V The peak voltage of the source is V₀ = V_ rms 2 = 50 2 V . Thus, the Assertion is true. Reason: In a series LCR circuit, the voltage across the inductor ( V_L ) leads the current by /2 , while the voltage across the capacitor ( V_C ) lags the current by /2 . Therefore, V_L and V_C are exactly radians ( 180^ ) out of phase. Their resultant, V_L - V_C , is either lead