Questions & Answers
Question
AnswersWhat is the Q factor of an LR circuit?
(A) $ \dfrac{1}{R} $
(B) $ \dfrac{{{X_L}}}{R} $
(C) 1
(D) 0
Answer
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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.
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
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