In series LCR circuit, the rms potential drop across R, L and C are V, 2 V and 2 V volts respectively. The source voltage is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → V
In a series LCR circuit the same current flows through all three elements. The voltage across R is in phase with the current, across L it leads by \( 90^\circ \) and across C it lags by \( 90^\circ \), so \( V_L \) and \( V_C \) are opposite in phase and the source voltage is their phasor sum:
\( V_{\mathrm{source}} = \sqrt{V_R^{2}+(V_L-V_C)^{2}} \)
\( V_{\mathrm{source}} = \sqrt{V^{2}+(2V-2V)^{2}} = V \)
The voltages across L and C are equal, so they cancel completely (the circuit is at resonance) and the source voltage equals the voltage across R.