SATHEE: Electromagnetic Induction and Alternating Current 6 Question 4

Electromagnetic Induction and Alternating Current 6 Question 4

4. For an $R - L - C$ circuit driven with voltage of amplitude $v_{m}$ and frequency $ω_{0} = \frac{1}{\sqrt{L C}}$ , the current exhibits resonance. The quality factor, $Q$ is given by

(2018 Main)

(a) $\frac{C R}{ω_{0}}$

(b) $\frac{ω_{0} L}{R}$

(d) $\frac{R}{ω_{0} C}$

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Answer:

Correct Answer: 4. (b)

Solution:

$Q = \frac{ω_{1} - ω_{2}}{ω_{0}}$

Here, $ω_{1} - ω_{2} =$ bandwidth $= \frac{R}{L}$

Substituting the values, we get

$Q = \frac{ω_{0} L}{R}$

Alternative solution $\frac{ω_{0} L}{R}$ is the only dimensionless quantity, hence it must be the quality factor.

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Electromagnetic Induction and Alternating Current 6 Question 4

4. For an R−L−C circuit driven with voltage of amplitude vm and frequency ω0=1LC, the current exhibits resonance. The quality factor, Q is given by

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4. For an $R - L - C$ circuit driven with voltage of amplitude $v_{m}$ and frequency $ω_{0} = \frac{1}{\sqrt{L C}}$ , the current exhibits resonance. The quality factor, $Q$ is given by