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(A) $ \dfrac{1}{R} $

(B) $ \dfrac{{{X_L}}}{R} $

(C) 1

(D) 0

Answer

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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.

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.

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