Question

An inductor and a resistor are connected in series to an ac supply. If the potential differences across the inductor and the resistor are 180 V and 240 V respectively, then the voltage of the ac supply is

• A. 300 V
• B. 420 V
• C. 60 V
• D. 210 V

Hint:

AC voltages add vectorially (phasors), not algebraically. $V_{total} \neq V_R + V_L$.

Answer 1

The Correct Option is A

Step 1: AC Circuit Formula:
In a series RL circuit connected to an AC source, the voltages across the resistor ($V_R$) and the inductor ($V_L$) are not in phase. $V_L$ leads $V_R$ by $90^\circ$. The total supply voltage $V$ is the phasor sum: \[ V = \sqrt{V_R^2 + V_L^2} \]
Step 2: Calculation:
Given $V_L = 180$ V and $V_R = 240$ V. \[ V = \sqrt{240^2 + 180^2} \] \[ V = \sqrt{57600 + 32400} = \sqrt{90000} \] \[ V = 300 \text{ V} \]