Electronics Engineering (ELEX) Board Practice Exam

When a solenoid coil with a resistance of 30 ohms and an inductance of 200 mH is connected to a 230 VAC, 50 Hz supply, what is the average power consumed?

1. 50 W

2. 227 W

3. 327 W

4. 430 W

The correct answer is: 327 W

To find the average power consumed by a solenoid coil with resistance and inductance connected to an AC supply, we need to calculate the total impedance of the coil and then use it to find the current flowing through the circuit. The impedance \( Z \) of an inductor in series with a resistor can be calculated using the formula: \[ Z = \sqrt{R^2 + (X_L)^2} \] where \( R \) is the resistance and \( X_L \) is the inductive reactance. The inductive reactance \( X_L \) is given by: \[ X_L = 2\pi f L \] Here, \( f \) is the frequency in hertz (Hz) and \( L \) is the inductance in henries (H). Given: - Resistance \( R = 30 \, \text{ohms} \) - Inductance \( L = 200 \, \text{mH} = 0.2 \, \text{H} \) - Frequency \( f = 50 \, \text{Hz} \) First, we calculate the inductive reactance \( X_L \): \[ X_L =