Which of the following is the expression for the mechanical power developed by the motor in terms of supply voltage?

Question

Question

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MPPGCL JE Electrical 28 April 2023 Shift 1 Official Paper

\(\rm V I_{a}-I_{a}^{2} R_{s h}\)
\(\mathrm{V} \mathrm{I}_{\mathrm{a}}-\mathrm{I}_{\mathrm{a}}^{2} \mathrm{R}_{\mathrm{a}}\)
\(\rm V I_{L}-I_{a}^{2} R_{a}\)
\(\mathrm{VI}_{\mathrm{L}}-\mathrm{I}_{\mathrm{L}}^{2} \mathrm{R}_{\mathrm{a}}\)

Answer 1

Concept

The given circuit is of a DC shunt motor.

In a DC motor, the input is electrical and the output is mechanical.

Electrical Input = Mechanical Output + Losses

Mechanical Output = Electrical Input - Losses

Explanation

Electrical Input = VI_a

Armature Losses = I_a²R

\(Mechanical \space Power = \mathrm{V} \mathrm{I}_{\mathrm{a}}-\mathrm{I}_{\mathrm{a}}^{2} \mathrm{R}_{\mathrm{a}}\)