Question 34: AC fundamentals

Question

A coil offers a resistance of $$20 \mathrm{~ohm}$$ 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 :

Accepted Answer

A coil typically offers a certain resistance to a direct current (DC), which is also known as its ohmic resistance. In the case of an alternating current (AC), the coil presents additional opposition to the flow of current, which is known as impedance. This impedance is due to both the ohmic resistance and the inductive reactance of the coil.
The inductive reactance $$X_L$$ of a coil in an AC circuit is given by the formula:
$$X_L = 2 \pi f L$$
where:
$$f$$ is the frequency of the alternating current
$$L$$ is the inductance of the coil
The total impedance $$Z$$ of the coil in an AC circuit, considering both the resistance $$R$$ and the inductive reactance $$X_L$$, is given by the formula:
$$Z = \sqrt{R^2 + X_L^2}$$
Since impedance $$Z$$ takes into account both ohmic resistance and inductive reactance, the resistance offered by the coil to an alternating current will always be greater than its resistance to a direct current, assuming the inductance $$L$$ is not zero.
Therefore, the resistance offered by the coil to the alternating current will be:
Option B: Greater than $$20 \Omega$$

Answer

$$0 \Omega$$

Answer

Greater than $$20 \Omega$$

Answer

Less than $$20 \Omega$$

Answer

$$20 \Omega$$

AC fundamentals

A coil offers a resistance of $20 \mathrm{~ohm}$ 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 :

Choose the correct answer: