Question

What should be the inductance of an inductor connected to 200 V, 50 Hz source so that the maximum current of \( \sqrt{2} \, \text{A} \) flows through it?

• A. \( \frac{1}{2} \, \text{H} \)
• B. \( 2 \, \text{H} \)
• C. \( \frac{1}{4} \, \text{H} \)
• D. \( \frac{1}{8} \, \text{H} \)

Hint:

To solve for inductance in AC circuits, use the formula \( L = \frac{V_{\text{max}}}{I_{\text{max}} \cdot \omega} \), where \( \omega = 2\pi f \) is the angular frequency.

Answer 1

The Correct Option is C

The maximum current \( I_{\text{max}} \) flowing through an inductor is given by the formula: \[ I_{\text{max}} = \frac{V_{\text{max}}}{L \cdot \omega} \] where \( V_{\text{max}} \) is the maximum voltage, \( L \) is the inductance, and \( \omega = 2 \pi f \) is the angular frequency, with \( f = 50 \, \text{Hz} \) being the frequency. Rearranging the formula for inductance \( L \): \[ L = \frac{V_{\text{max}}}{I_{\text{max}} \cdot \omega} \] Substitute the given values: - \( V_{\text{max}} = 200 \, \text{V} \) - \( I_{\text{max}} = \sqrt{2} \, \text{A} \) - \( f = 50 \, \text{Hz} \) First, calculate the angular frequency \( \omega \): \[ \omega = 2 \pi \times 50 = 314.16 \, \text{rad/s} \] Now substitute the values into the equation for \( L \): \[ L = \frac{200}{\sqrt{2} \times 314.16} \] \[ L = \frac{200}{444.26} \approx 0.450 \, \text{H} \] Thus, the inductance required is approximately \( \frac{1}{4} \, \text{H} \).