Question:
In an AC circuit, supply voltage \( V_{\text{rms}} = 1000\,\text{V} \), \( R = 80\,\Omega \), \( X_L = 80\,\Omega \), and source frequency \( f = 50\,\text{Hz} \). Find the power factor.
In an AC circuit, supply voltage \( V_{\text{rms}} = 1000\,\text{V} \), \( R = 80\,\Omega \), \( X_L = 80\,\Omega \), and source frequency \( f = 50\,\text{Hz} \). Find the power factor.
Updated On: Apr 8, 2026
- \( \dfrac{1}{\sqrt{2}} \)
- \( \dfrac{1}{\sqrt{3}} \)
- \( \dfrac{1}{\sqrt{5}} \)
- \( \dfrac{1}{\sqrt{6}} \)
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The Correct Option is A
Solution and Explanation
Concept:
In an AC circuit containing resistance and inductance (R–L circuit), the power factor is given by
\[
\cos\phi = \frac{R}{Z}
\]
where
Step 2: Calculate the power factor.} \[ \cos\phi = \frac{R}{Z} \] Substituting the values: \[ \cos\phi = \frac{80}{80\sqrt{2}} \] \[ \cos\phi = \frac{1}{\sqrt{2}} \] Final Result \[ \text{Power factor} = \frac{1}{\sqrt{2}} \]
- \(R\) = Resistance
- \(Z\) = Impedance of the circuit
- \(Z = \sqrt{R^2 + X_L^2}\)
- \(X_L\) = Inductive reactance
Step 2: Calculate the power factor.} \[ \cos\phi = \frac{R}{Z} \] Substituting the values: \[ \cos\phi = \frac{80}{80\sqrt{2}} \] \[ \cos\phi = \frac{1}{\sqrt{2}} \] Final Result \[ \text{Power factor} = \frac{1}{\sqrt{2}} \]
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