In a series LCR circuit if the voltage across inductor, capacitor and resistor respectively are 60 V, 30 V and 40 V, then the applied voltage is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 50 V
In a series LCR circuit the voltages across the elements 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, and their difference is at right angles to \( V_R \).
\( \displaystyle V = \sqrt{V_R^{2}+(V_L-V_C)^{2}} = \sqrt{40^{2}+(60-30)^{2}}\,\mathrm{V} = \sqrt{1600+900}\,\mathrm{V} = 50\,\mathrm{V} \)
Shortcut: The two sides 30 V and 40 V belong to the 3-4-5 right triangle, so the hypotenuse is 50 V at once.