Question

What is the Q factor of an LR circuit?
(A) $\dfrac{1}{R}$
(B) $\dfrac{{{X_L}}}{R}$
(C) 1
(D) 0

Answer 1

The Q factor of the LR circuit is inversely proportional to resistance and is directly proportional to inductive reactance.

Complete step by step solution
The quality factor or Q factor of an LR circuit at the operating frequency $\omega$ is defined as the ratio of reactance $\nu F$ of the coil to the resistance.
We can use the above definition to write the formula of the Q factor of the LR circuit.
$Q = \dfrac{{\omega L}}{R} = \dfrac{{{X_L}}}{R}$
Where ${X_L}$ is the inductive reactance of the coil and $R$ is the resistance.
This implies that option B is correct.

Additional information
Inductive reactance, which is also known by the symbol, ${X_L}$ , is the property in an AC circuit that opposes the change in the current.
We can write an equation for inductive reactance which would be as follows.
${X_L} = 2\pi fL$
Where f is the frequency and L is the inductance of the coil and we can further write $2\pi f$ as $\omega$
Then, the equation can be written in a simpler form as
${X_L} = \omega L$
Where $\omega$ is the angular velocity.
The Q factor is a unitless and dimensionless quantity.

Note
The more resistance there will be, the less will be the value of the Q factor. We can also say that as inductive reactance is frequency-dependent, at DC, an inductor will have zero reactance, and therefore the Q factor will have to be zero, and at high frequencies, an inductor has an infinite reactance