Given below are two electric circuits A and B.

Calculate the ratio of power factor of the circuit B to the power factor of circuit A.

Solution

For circuit 1 we have,

$z = \sqrt{{X_{L}}^{2} + R^{2}} = \sqrt{(3 R)^{2} + R^{2}} = R \sqrt{10}$
Therefore,
Power factor, $\cos ϕ = \frac{R}{Z} = \frac{R}{R \sqrt{10}} = \frac{1}{\sqrt{10}}$
For circuit 2 we have,

$Z' = \sqrt{R^{2} + (X_{L} - X_{C})^{2}} = \sqrt{R^{2} + (3 R - R)^{2}} = R \sqrt{5}$
Therefore,
Power factor, $\cos ϕ' = \frac{R}{Z'} = \frac{R}{R \sqrt{5}} = \frac{1}{\sqrt{5}}$
Thus, the ratio of the power factor is given by,

$\frac{\cos ϕ'}{\cos ϕ} = \frac{\sqrt{10}}{\sqrt{5}} = \frac{\sqrt{5 \times 2}}{\sqrt{5}} = \sqrt{2} : 1$

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Given below are two electric circuits A and B.

Calculate the ratio of power factor of the circuit B to the power factor of circuit A.

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Electrostatic Potential And Capacitance

Given below are two electric circuits A and B.Calculate the ratio of power factor of the circuit B to the power factor of circuit A.

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Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Given below are two electric circuits A and B.

Calculate the ratio of power factor of the circuit B to the power factor of circuit A.