Question

An AC source is connected to a resistor and an inductor in series. The voltage across the resistor and inductor are 8 V and 6 V respectively. The voltage of the source is:

• A. 10 V
• B. 12 V
• C. 14 V
• D. 16 V

Hint:

In AC circuits with resistors and inductors, use the Pythagorean sum of voltages: \( V = \sqrt{V_R^2 + V_L^2} \) due to phase difference.

Answer 1

The Correct Option is A

In an R-L series AC circuit, the total voltage is not the simple algebraic sum of the voltages across the resistor and inductor due to their phase difference. The voltage across the resistor is in phase with the current, while the voltage across the inductor leads the current by \(90^\circ\). Consequently, the total voltage is the phasor sum of the individual voltages: \[V_{\text{source}} = \sqrt{V_R^2 + V_L^2}\] With the given values \( V_R = 8 \, \text{V} \) and \( V_L = 6 \, \text{V} \): \[V_{\text{source}} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \, \text{V}\]