Question

An electric motor operates on a $50~\mathrm{V}$ supply and a current of $12\mathrm{A}$. If the efficiency of the motor is $30%$, what is the resistance of the winding of the motor?

• A. $6\Omega$
• B. $4\Omega$
• C. $2.9\Omega$
• D. $3.1\Omega$

Hint:

Motor efficiency $\eta = \frac{\text{output}}{\text{input}}$, loss = $I^2R$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Motor efficiency $\eta = \frac{\text{output}}{\text{input}}$, loss = $I^2R$.
Step 2: Detailed Explanation:
Input power = $VI = 50 \times 12 = 600$ W. Output power = efficiency $\times$ input = $0.3 \times 600 = 180$ W. Power loss in winding = $I^2R = 600 - 180 = 420$ W. So $R = \frac{420}{12^2} = \frac{420}{144} = 2.92 \approx 2.9\Omega$.
Step 3: Final Answer:
The resistance of the winding is $2.9\Omega$.