In a series LCR circuit, an ac voltmeter reads 20 V across the resistor, 30 V across the inductor and 15 V across the capacitor. The supply voltage is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 25 V
In a series LCR circuit the same current flows through every element, but the voltages across them are not in phase.
\( V_R \) is in phase with the current. \( V_L \) leads it by \( 90^\circ \), and \( V_C \) lags it by \( 90^\circ \). So \( V_L \) and \( V_C \) are opposite to each other.
The supply voltage is the phasor sum of the three voltages. They are added as vectors.
Its value is:
\( \begin{aligned} V &= \sqrt{V_R^2+(V_L-V_C)^2} \\ &= \sqrt{(20\,\mathrm{V})^2+(30\,\mathrm{V}-15\,\mathrm{V})^2} \\ &= \sqrt{400+225}\,\mathrm{V} \\ &= 25\,\mathrm{V} \end{aligned} \)