Correct Answer

Direct FormulaElectricalBasic Electrical

Option A

Quick Summary: Given: Resistance R = 25 Ohm, Impedance Z = 50 Ohm

📋 Given

Resistance R = 25 Ohm, Impedance Z = 50 Ohm

🔢 Formula Used

cos⁡(ϕ)=RZ\cos(\phi) = \frac{R}{Z}cos(ϕ)=ZR​

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify given parameters

We are provided with the resistance ( $R$ ) and the impedance ( $Z$ ) of the AC circuit.

R=25Ω,Z=50ΩR = 25 \Omega, Z = 50 \OmegaR=25Ω,Z=50Ω

Recall the power factor formula

The power factor in an AC circuit is defined as the ratio of resistance to impedance.

cos⁡(ϕ)=RZ\cos(\phi) = \frac{R}{Z}cos(ϕ)=ZR​

Calculate the power factor

Substitute the given values into the formula to find the power factor.

cos⁡(ϕ)=2550=0.5\cos(\phi) = \frac{25}{50} = 0.5cos(ϕ)=5025​=0.5

✅

B is correct because the power factor is the ratio of resistance to impedance, which yields 0.5 for the given values.

Core Concepts Used

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AC Circuits Impedance Triangle Power Factor

💡 EXAM TIP

In AC power analysis, remember that the power factor is also equal to $\cos(\phi)$ , where $\phi$ is the phase angle between voltage and current; this is fundamental for calculating real power $P = VI \cos(\phi)$ .

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