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 (resistor-inductor) series AC circuit, the total voltage is not the algebraic sum of the voltages across the resistor and inductor. This is because the voltages are out of phase: - Voltage across the resistor is in phase with current. - Voltage across the inductor leads the current by \(90^\circ\). So, the total voltage is the phasor sum of the two voltages: \[ V_{\text{source}} = \sqrt{V_R^2 + V_L^2} \] Given: \( V_R = 8 \, \text{V} \), \( V_L = 6 \, \text{V} \) \[ V_{\text{source}} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \, \text{V} \]