Question

Q-Factor at resonance is given by ICA O ILLO VICO VLIV O

Answer 1

$\text{ Ans}\text{ (d)}\text{ }\text{V}_\text{L}/\text{V}$

Explanation:

We know the Q factor in LCR circuit is defined as the sharpness of resonance and it is defined as the ratio of the inductive reactance or capacitative reactance at resonance and resresistance.

$\text{ Q}\text{ factor}=\frac{\omega_0 L}{R} = \frac{1}{\omega_0CR}$

$\text{or},\text{ Q}\text{ factor}=\frac{X_L}{R} = \frac{X_C}{R}$

$\text{or},\text{ Q}\text{ factor}=\frac{IX_L}{IR} = \frac{IX_C}{IR}=\frac{V_L}{V}=\frac{V_C}{V}$

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so we get, Q factor =

why other options are not correct:

(a)

$I_C=\frac{V}{X_C}=\frac{V}{\frac{1}{\omega_0 C}}=V\omega_0C$$\text{Q}\text{ factor}=\frac{1}{\omega_0 CR}=\frac{V}{\omega_0 CRV}=\frac{V}{I_cR}=\frac{I}{I_C}$

So, Q=Ic/I cannot be corrected.

(b)

$I_L=\frac{V}{X_L}=\frac{V}{\omega_0 L}$

$Q \text{ factor}=\frac{\omega_0L}{R}=\frac{V}{I_L R}=\frac{I}{I_L}$

So, Q= Il/I cannot be corrected.

(c) from above calculation we see ,

Q=Vc/V

So Q=V/Vc cannot be corrected.