In the following circuit, calculate,
(i) the capacitance 'c' of the capacitor if the power factor of the circuit is unity, and
(ii) also calculate the Q-factor of the circuit.

Solution

(i) Power factor is given by,

$\cos ϕ = \frac{R}{Z} or Z = R$

[For power factor unity $\cos θ = 1$ ]

$∴$ $X_{C} = X_{L} or \frac{1}{2 πfC} = 2 πfL$

$C = \frac{1}{4 π^{2} f^{2} L} = \frac{1}{4 \times 9.87 \times (50)^{2} \times 200 \times 10^{- 3}}$

$= 5 \times 10^{- 5} F$

$C = 50 μF .$

(ii) Quality factor of the circuit is given by,

$Q - factor = \frac{1}{R} \sqrt{\frac{L}{C}}$

$Q = \frac{1}{10} \sqrt{\frac{200 \times 10^{- 3}}{5 \times 10^{- 5}}} = 6.32$

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Electrostatic Potential And Capacitance

In the following circuit, calculate,
(i) the capacitance 'c' of the capacitor if the power factor of the circuit is unity, and
(ii) also calculate the Q-factor of the circuit.

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Electrostatic Potential And Capacitance

In the following circuit, calculate,(i) the capacitance 'c' of the capacitor if the power factor of the circuit is unity, and(ii) also calculate the Q-factor of the circuit.

Some More Questions From Electrostatic Potential and Capacitance Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

In the following circuit, calculate,
(i) the capacitance 'c' of the capacitor if the power factor of the circuit is unity, and
(ii) also calculate the Q-factor of the circuit.