Question

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

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Hint: 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.

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.
${X_L} = 2\pi fL$
Where f is the frequency and L is the inductance of the coil and we can further write $2\pi f$ as $\omega$
${X_L} = \omega L$
Where $\omega$ is the angular velocity.