Correct Answer

Direct FormulaElectricalBasic Electrical

Option A

Quick Summary: Given: Resistance R = 50 ohm, Impedance Z = 50 ohm.

📋 Given

Resistance R = 50 ohm, Impedance Z = 50 ohm.

🔢 Formula Used

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

🔢 Step-by-Step Solution

Identify Given Parameters

We are given the resistance $R = 50\ \Omega$ and the total impedance of the circuit $Z = 50\ \Omega$ .

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

State Power Factor Formula

The power factor (p.f.) of an AC circuit is defined as the ratio of resistance to impedance.

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

Calculate the Power Factor

Substituting the given values into the formula: $\text{p.f.} = \frac{50}{50} = 1$ .

p.f.=5050=1\text{p.f.} = \frac{50}{50} = 1p.f.=5050​=1

✅

C is correct because the power factor is the ratio of resistance to impedance, which in this case is 50/50 = 1.

Core Concepts Used

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AC Circuits Power Factor Impedance Triangle

💡 EXAM TIP

A power factor of 1 indicates a purely resistive circuit where voltage and current are in phase, commonly tested alongside resonance conditions where inductive and capacitive reactances cancel out.

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