Question

200 V, 50 Hz inductive circuit takes a current of 10 A lagging the voltage by 30°. Calculate inductance of the circuit.

• A. 31.85 mH
• B. 51.85 mH
• C. 21.85 mH
• D. 11.85 mH

Hint:

For inductive circuits, use the relationship between voltage, current, and inductive reactance to calculate the inductance: \( X_L = \frac{V}{I \sin(\theta)} \) and \( X_L = 2\pi f L \).

Answer 1

The Correct Option is A

Given: - Voltage \( V = 200 \, \text{V} \) - Current \( I = 10 \, \text{A} \) - Frequency \( f = 50 \, \text{Hz} \) - Phase angle \( \theta = 30^\circ \) The formula for the inductive reactance \( X_L \) is: \[ X_L = \frac{V}{I \sin(\theta)} \] Substituting the known values: \[ X_L = \frac{200}{10 \sin(30^\circ)} = \frac{200}{10 \times 0.5} = 40 \, \Omega \] The inductance \( L \) is related to the inductive reactance by: \[ X_L = 2 \pi f L \] Solving for \( L \): \[ L = \frac{X_L}{2 \pi f} = \frac{40}{2 \pi \times 50} = \frac{40}{314.16} \approx 0.127 \, \text{H} = 31.85 \, \text{mH} \] Thus, the inductance of the circuit is 31.85 mH.