Question

If impedance is \( \sqrt{3} \) times resistance, then find phase difference.

• A. Zero
• B. \(30^\circ\)
• C. \(60^\circ\)
• D. Data is incomplete

Hint:

Use \( \tan \phi = \frac{X}{R} \) and \( Z = \sqrt{R^2 + X^2} \) in AC circuits to find the phase angle when impedance and resistance are known.

Answer 1

The Correct Option is C

In an AC circuit containing resistance \( R \) and reactance \( X \), the impedance \( Z \) is given by: \[ Z = \sqrt{R^2 + X^2} \] We are given: \[ Z = \sqrt{3} R \] So, \[ \sqrt{R^2 + X^2} = \sqrt{3} R \Rightarrow R^2 + X^2 = 3R^2 \Rightarrow X^2 = 2R^2 \Rightarrow X = \sqrt{2} R \] Now, the phase angle \( \phi \) is given by: \[ \phi = \tan^{-1} \left( \frac{X}{R} \right) = \tan^{-1} (\sqrt{2}) \] \[ \tan \phi = \sqrt{2} \Rightarrow \phi = 60^\circ \] Therefore, the phase difference is \( \boxed{60^\circ} \).