What is the correction factor of the wattmeter at a lagging power factor?

(Where, φ is the phase angle between the voltage applied to the pressure coil and the current in the current coil and β is the angle between the voltage applied to the pressure coil and the current in the pressure coil.)

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SSC JE Electrical 05 Jun 2024 Shift 3 Official Paper - 1
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  1. \(\rm \frac{cos\Phi}{cos \beta \,cos (\Phi - \beta)}\)
  2. \(\rm \frac{cos\Phi}{cos \beta \,sin (\Phi + \beta)}\)
  3. \(\rm \frac{cos\Phi}{cos \beta \,sin (\Phi - \beta)}\)
  4. \(\rm \frac{cos\Phi}{cos \beta \,cos (\Phi + \beta)}\)

Answer (Detailed Solution Below)

Option 1 : \(\rm \frac{cos\Phi}{cos \beta \,cos (\Phi - \beta)}\)
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Detailed Solution

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Correction factor: The ratio of True reading (W t ) to Actual reading (W a ) is known as Correction factor of the wattmeter.

 W t =  \(\frac{VI_1}{R}Cos(\phi)\)

and, Wa = \({\frac{VI_1}{R}Cos(\alpha)Cos(\phi-\beta)}\)

Where φ is the phase angle between the voltage applied to the pressure coil and the current in the current coil and β is the angle between the voltage applied to the pressure coil and the current in the pressure coil

Correction factor = \(\frac{\frac{VI_1}{R}Cos(\phi)}{\frac{VI_1}{R}Cos(\beta)Cos(\phi-\beta)}\)= \(\frac{Cos(\phi)}{Cos(\beta)Cos(\phi-\beta)}\)

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