To determine the resistance of the winding of the motor, we must use the given parameters: voltage supply \(V = 50 \, \text{V}\), current \(I = 12 \, \text{A}\), and efficiency \(30\%.\)
The efficiency formula for an electric motor is given by:
\(\eta = \frac{\text{Output Power}}{\text{Input Power}} \times 100\%\)
Where:
Calculate the input power:
\(\text{Input Power} = 50 \, \text{V} \times 12 \, \text{A} = 600 \, \text{W}\)
Now, find the output power using the energy efficiency:
\(30\% = \frac{\text{Output Power}}{600 \, \text{W}} \times 100\%\)
So,
\(\text{Output Power} = \frac{30}{100} \times 600 \, \text{W} = 180 \, \text{W}\)
The power loss can be calculated as the difference between the input power and the output power:
\(\text{Power Loss} = \text{Input Power} - \text{Output Power} = 600 \, \text{W} - 180 \, \text{W} = 420 \, \text{W}\)
The power loss in the winding is given by heat due to the resistance:
\(\text{Power Loss} = I^2 \times R\)
Therefore, to find the resistance \(R\), we rearrange the equation:
\(R = \frac{\text{Power Loss}}{I^2} = \frac{420 \, \text{W}}{12^2 \, \text{A}^2} = \frac{420}{144} \, \Omega = 2.9167 \, \Omega\)
Rounding off to one decimal place, the resistance is approximately \(2.9 \, \Omega\).
Thus, the correct answer is \(2.9 \, \Omega\). This corresponds to the given answer option.