A series LCR circuit is connected to an ac source. If the voltage across the inductor, capacitor and resistor are \( 50\ \mathrm{V} \), \( 20\ \mathrm{V} \) and \( 40\ \mathrm{V} \), respectively, then the applied source voltage is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 50\ \mathrm{V} \)
In a series LCR circuit the voltages across L and C are opposite in phase, and both are at \( 90^{\circ} \) to the voltage across R. So they are added as phasors, not arithmetically.
\( \displaystyle V = \sqrt{V_{R}^{2}+(V_{L}-V_{C})^{2}} \)
\( \displaystyle V = \sqrt{(40\,\mathrm{V})^{2}+(50\,\mathrm{V}-20\,\mathrm{V})^{2}} \)
\( \displaystyle V = \sqrt{1600+900}\,\mathrm{V} = 50\,\mathrm{V} \)