Question

An inductor and a resistor are connected in series to an AC source of 10 V. If the potential difference across the inductor is 6 V, then the potential difference across the resistor is

• A. \( 4 \, \text{V} \)
• B. \( 10 \, \text{V} \)
• C. \( 6 \, \text{V} \)
• D. \( 8 \, \text{V} \) \bigskip

Hint:

In a series circuit, the total potential difference is the sum of the individual potential differences across the components.

Answer 1

The Correct Option is D

Step 1: Understanding AC Circuit Voltage Relations For an AC circuit consisting of a resistor (R) and inductor (L) in series, the total voltage (\( V \)) is given by the phasor sum of the voltage across the resistor (\( V_R \)) and the inductor (\( V_L \)): \[ V_{\text{rms}}^2 = V_R^2 + V_L^2 \] where: - \( V_{\text{rms}} \) = total voltage supplied by the AC source = \( 10 \) V - \( V_L \) = voltage across the inductor = \( 6 \) V - \( V_R \) = voltage across the resistor (to be determined)

Step 2: Applying the Phasor Equation \[ 10^2 = V_R^2 + 6^2 \] \[ 100 = V_R^2 + 36 \] \[ V_R^2 = 100 - 36 = 64 \] \[ V_R = \sqrt{64} = 8 \text{ V} \] Thus, the potential difference across the resistor is: \[ \mathbf{8 \, \text{V}} \]