Question

A coil offers a resistance of 20 ohms for a direct current. If we send an alternating current through the same coil, the resistance offered by the coil to the alternating current will be:

• A. 0\(\Omega\)
• B. Greater than 20\(\Omega\)
• C. Less than 20\(\Omega\)
• D. 20\(\Omega\)

Hint:

When working with coils and alternating current, remember that inductance adds to the total opposition to the current, making the impedance greater than the resistance for DC.

Answer 1

The Correct Option is B

For a direct current (DC), the resistance of the coil is given as 20 ohms. However, when an alternating current (AC) flows through the same coil, the total resistance offered by the coil is affected by both the resistance of the wire and the inductance of the coil. The coil's inductance creates inductive reactance, which increases the total opposition to the alternating current. 
The total resistance to AC is called the impedance, which is given by: \[ Z = \sqrt{R^2 + X_L^2} \] where \( R \) is the resistance (20 ohms in this case), and \( X_L \) is the inductive reactance. Since \( X_L \) is always positive, the impedance will always be greater than the resistance \( R \) when AC flows through the coil. Therefore, the resistance offered by the coil to the alternating current will be greater than 20 ohms. 
Thus, the correct answer is \(\text{Greater than 20\(\Omega\)}\).