An electric motor operating on a 50 V dc supply draws a current of 12 A. If the efficiency of the motor is 30%, the estimated resistance of the motor would be:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 2.9 Ω
The electrical power taken from the supply is \( P_{\mathrm{in}} = VI \). A fraction equal to the efficiency becomes useful mechanical power, and the rest is lost as heat in the resistance of the winding, \( P_{\mathrm{loss}} = I^{2}R \).
\( P_{\mathrm{in}} = 50\,\mathrm{V}\times12\,\mathrm{A} = 600\,\mathrm{W} \)
\( P_{\mathrm{out}} = 0.30\times600\,\mathrm{W} = 180\,\mathrm{W} \)
\( P_{\mathrm{loss}} = 600 - 180 = 420\,\mathrm{W} \)
\( \displaystyle R = \frac{P_{\mathrm{loss}}}{I^{2}} = \frac{420\,\mathrm{W}}{(12\,\mathrm{A})^{2}} = \frac{420}{144}\,\Omega \approx 2.9\,\Omega \)