Question 33: AC fundamentals

Question

A coil of inductance $$1 \mathrm{H}$$ and resistance $$100 \Omega$$ is connected to an alternating current source of frequency $$\frac{50}{\pi} \mathrm{~Hz}$$. What will be the phase difference between the current and voltage?

Accepted Answer

The phase difference between the current and the voltage in an AC circuit containing resistance and inductance (RL circuit) depends on the values of the resistance (R) and inductive reactance (X
L
).
The inductive reactance is given by the formula:
$$X_L = 2 \pi f L$$
where:
$$f$$ is the frequency of the AC source
$$L$$ is the inductance of the coil
Substituting the given values:
$$f = \frac{50}{\pi} 	ext{ Hz}$$
$$L = 1 	ext{ H}$$
We get:
$$X_L = 2 \pi \left( \frac{50}{\pi} ight) 	imes 1$$
$$X_L = 100 \ \Omega$$
The phase angle $$\phi$$ between the current and the voltage is given by the equation:
$$	an \phi = \frac{X_L}{R}$$
Given:
$$R = 100 \ \Omega$$
So:
$$	an \phi = \frac{100}{100} = 1$$
The angle $$\phi$$ whose tangent is 1 is 45 degrees:
$$\phi = 45^\circ$$
Thus, the phase difference between the current and voltage is 45 degrees.
The correct answer is Option D: 45$$^\circ$$
.

Answer

90$$^\circ$$

Answer

30$$^\circ$$

Answer

60$$^\circ$$

Answer

45$$^\circ$$

AC fundamentals

A coil of inductance $1 \mathrm{H} and resistance 100 \Omega is connected to an alternating current source of frequency \frac{50}{\pi} \mathrm{~Hz}$. What will be the phase difference between the current and voltage?

Choose the correct answer: