Question

The impedance of a circuit consists of \(3 \Omega\) resistance and \(4 \Omega\) reactance. The power factor of the circuit is. (a) \(0.4\) (b) \(0.6\) (c) \(0.8\) (d) \(1.0\)

Short answer

The power factor of the circuit can be calculated using the formula Power Factor = \(cos(\theta)\) = \(\frac{R}{Z}\). First, calculate the impedance Z with the given resistance R and reactance X: \(Z = \sqrt{R^2 + X^2} = \sqrt{(3 \Omega)^2 + (4 \Omega)^2} = 5 \Omega\). Then, find the power factor: Power Factor = \(\frac{3 \Omega}{5 \Omega} = 0.6\). The correct answer is (b) 0.6.

Step-by-step solution

Calculate the impedance

To calculate the impedance, use the formula: \(Z = \sqrt{R^2 + X^2}\) Plug in the given resistance and reactance values: \(Z = \sqrt{(3 \Omega)^2 + (4 \Omega)^2}\)

Simplify the expression

Evaluate the squares and sum inside the square root: \(Z = \sqrt{9 + 16}\) Add the numbers inside the square root: \(Z = \sqrt{25}\) Take the square root of 25: \(Z = 5 \Omega\)

Calculate the power factor

Now that we have the impedance, we can find the power factor using the formula: Power Factor = \(cos(\theta)\) = \(\frac{R}{Z}\) Plug in the given resistance and calculated impedance values: Power Factor = \(\frac{3 \Omega}{5 \Omega}\)

Simplify the expression

Divide 3 by 5 to get the power factor: Power Factor = \(0.6\) The power factor of the circuit is 0.6, so the correct answer is (b) 0.6.