Obtain the resonant frequency ωr of a series LCR circuit with L = 2.0H, C = 32 µF and R = 10 Ω. What is the Q-value of this circuit?

Home » Obtain the resonant frequency ωr of a series LCR circuit with L = 2.0H, C = 32 µF and R = 10 Ω. What is the Q-value of this circuit?

Obtain the resonant frequency ωr of a series LCR circuit with L = 2.0H, C = 32 µF and R = 10 Ω. What is the Q-value of this circuit?

The inductance of the inductor can be considered as $L=2.0H$

The capacitance of the capacitor will be , $C=32\mu F=32\times {{10}^{-6}}F$

The resistance of the resistor as per question is $R=10\Omega$

As we know, resonant frequency can be calculated by the relation given below,

${{\omega }_{r}}=\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{2\times 32\times {{10}^{-6}}}}=\frac{1}{8\times {{10}^{-6}}}=125\frac{rad}{\sec }$

Now, Q – value of the circuit can be calculated by the relation stated below:

$Q=\frac{1}{R} \sqrt{\frac{L}{C}}=\frac{1}{10} \sqrt{\frac{2}{32 \times 10^{-6}}}=\frac{1}{10 \times 4 \times 10^{-3}}=25$

Thus , the Q – value of the question given above will be 25

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