Case: Read the passage and answer the question.
A DC motor draws a current of 20 A from a 115 V supply and delivers a mechanical power of 1700 W. Assume that the rest of the power drawn is dissipated as heat in the resistance of the motor.
Estimate the resistance of the motor.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 1.5\,\Omega \)
The electrical power drawn from the supply is \( P=VI \). Part of it is delivered as mechanical power, and the rest is dissipated as heat in the resistance of the motor at the rate \( I^{2}R \).
The power drawn from the supply is:
\( \begin{aligned} P_{\mathrm{in}} &= VI \\ &= 115\,\mathrm{V}\times20\,\mathrm{A} \\ &= 2300\,\mathrm{W} \end{aligned} \)
The power dissipated as heat is:
\( \begin{aligned} P_{\mathrm{heat}} &= P_{\mathrm{in}}-P_{\mathrm{mech}} \\ &= 2300\,\mathrm{W}-1700\,\mathrm{W} \\ &= 600\,\mathrm{W} \end{aligned} \)
Since \( P_{\mathrm{heat}}=I^{2}R \), the resistance of the motor is:
\( \begin{aligned} R &= \frac{P_{\mathrm{heat}}}{I^{2}} \\ &= \frac{600\,\mathrm{W}}{(20\,\mathrm{A})^{2}} \\ &= 1.5\,\Omega \end{aligned} \)