The resistance of a coil for dc is in ohms. In ac, the resistance (a) will remain same (b) will increase (c) will decrease (d) will be zero

Impedance is the measure of opposition a circuit offers to the flow of alternating current (AC). It is represented by the symbol Z and is a complex number combining both resistance (R) and reactance (X). The magnitude of the impedance is given by \(|Z| = \sqrt{R^2 + X^2}\), where R is the resistance and X is the reactance.

A coil is an inductor, and in AC circuits, an inductor exhibits inductive reactance along with its resistance. Inductive reactance (X_L) is a property of an inductor that opposes the change in current and is given by the formula \(X_L = 2 \pi f L\), where f is the frequency of the AC and L is the inductance of the coil.

We now need to calculate the impedance (Z) for the coil in an AC circuit using its resistance (R) and inductive reactance (X_L). The magnitude of the impedance Z is given by the formula \(|Z| = \sqrt{R^2 + (X_L)^2}\).

Since the inductive reactance (X_L) is always greater than or equal to zero (\(X_L \geq 0\)), it follows that \(|Z| \geq R\). As a result, the impedance of a coil in an AC circuit will be greater than or equal to its resistance in a DC circuit. Considering the options provided: (a) will remain the same: This could only be true if X_L = 0 (no reactive component), which is not the case for a coil. (b) will increase: This is the correct answer, as the impedance (Z) will always be higher than the resistance (R) due to the additional inductive reactance (X_L) in the AC circuit. (c) will decrease: This is not true, as the impedance (Z) will always be higher than the resistance (R) due to the inductive reactance (X_L) in the AC circuit. (d) will be zero: This is also not true, as the coil still has resistance (R) and inductive reactance (X_L) that both contribute to the impedance in an AC circuit.

The correct answer is (b) the resistance of a coil in an AC circuit will increase compared to its resistance in a DC circuit.