An electric motor operates on a 50 volt supply and draws a current of 12 A. If the efficiency of the motor is 30%, find the resistance of the windings of the motor.

• A) 3.4Ω
• B) 2.1Ω
• C) 3.9Ω
• D) 2.9Ω

To find the resistance of the windings of the motor, we first need to calculate the input power and the output power based on the efficiency. The formula for electrical power is:

Calculating Input Power

The input power (P_in) can be calculated using the formula:

P_in = Voltage × Current

Substituting the given values:

P_in = 50 V × 12 A = 600 W

Calculating Output Power

Next, we find the output power (P_out) using the efficiency:

Efficiency = (P_out / P_in) × 100%

Rearranging gives us:

P_out = Efficiency × P_in / 100

Substituting the values:

P_out = 30% × 600 W / 100 = 180 W

Finding the Resistance

Now, we can find the power loss due to resistance (P_loss), which is the difference between input power and output power:

P_loss = P_in - P_out = 600 W - 180 W = 420 W

Using Ohm's Law

According to Ohm's Law, the power loss in the windings can also be expressed as:

P_loss = I² × R

Where I is the current and R is the resistance. Rearranging gives:

R = P_loss / I²

Substituting the values:

R = 420 W / (12 A)² = 420 W / 144 A² = 2.92 Ω

Final Answer

The resistance of the windings of the motor is approximately 2.9Ω. Therefore, the correct option is D) 2.9Ω.