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If the resonant frequency in a series RLC circuit is 50kHz along with a bandwidth of 1kHz, find the quality factor.
- a)5
- b)50
- c)100
- d)500
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If the resonant frequency in a series RLC circuit is 50kHz along with ...
We know that Quality factor is equal to the resonant frequency divided by the bandwidth. Substituting the values from the given question, we get Q=50.
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If the resonant frequency in a series RLC circuit is 50kHz along with ...
To find the quality factor (Q) of a series RLC circuit, we need to use the formula:
Q = fr / BW
Where fr is the resonant frequency and BW is the bandwidth.
Given:
Resonant frequency (fr) = 50 kHz
Bandwidth (BW) = 1 kHz
Now, let's substitute the given values into the formula:
Q = 50 kHz / 1 kHz
Simplifying this expression, we get:
Q = 50
Therefore, the quality factor (Q) of the series RLC circuit is 50.
Explanation:
The quality factor (Q) of a series RLC circuit determines the sharpness of the resonance curve. It is defined as the ratio of the resonant frequency (fr) to the bandwidth (BW).
In this case, the resonant frequency is given as 50 kHz and the bandwidth is given as 1 kHz. By substituting these values into the formula, we find that the quality factor is 50.
A higher quality factor indicates a narrower bandwidth and a sharper resonance curve. This means that the circuit can more effectively filter out frequencies that are not at the resonant frequency.
In this circuit, the resonant frequency is 50 kHz, and the bandwidth is 1 kHz. This means that the circuit is able to effectively filter out frequencies that are not close to the resonant frequency of 50 kHz.
Therefore, the correct answer is option B) 50.
Q = fr / BW
Where fr is the resonant frequency and BW is the bandwidth.
Given:
Resonant frequency (fr) = 50 kHz
Bandwidth (BW) = 1 kHz
Now, let's substitute the given values into the formula:
Q = 50 kHz / 1 kHz
Simplifying this expression, we get:
Q = 50
Therefore, the quality factor (Q) of the series RLC circuit is 50.
Explanation:
The quality factor (Q) of a series RLC circuit determines the sharpness of the resonance curve. It is defined as the ratio of the resonant frequency (fr) to the bandwidth (BW).
In this case, the resonant frequency is given as 50 kHz and the bandwidth is given as 1 kHz. By substituting these values into the formula, we find that the quality factor is 50.
A higher quality factor indicates a narrower bandwidth and a sharper resonance curve. This means that the circuit can more effectively filter out frequencies that are not at the resonant frequency.
In this circuit, the resonant frequency is 50 kHz, and the bandwidth is 1 kHz. This means that the circuit is able to effectively filter out frequencies that are not close to the resonant frequency of 50 kHz.
Therefore, the correct answer is option B) 50.
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