Question

Efficiency of electric motor can be represented as

• A. \(\frac{T \omega}{V I}\)
• B. \(\frac{T I}{V \omega}\)
• C. \(\frac{T \omega}{T V}\)
• D. \(\frac{I \omega}{V I}\)

Hint:

Output = Mechanical ($\text{Torque} \times \text{Angular velocity}$).
Input = Electrical ($\text{Voltage} \times \text{Current}$).
Efficiency is always $\frac{\text{Output}}{\text{Input}} = \frac{T\omega}{VI}$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The efficiency of any electrical machine is defined as the ratio of useful mechanical output power to the total electrical input power supplied to the motor.
Key Formula or Approach:
\[ \eta = \frac{P_{\text{out}}}{P_{\text{in}}} \times 100\% \]
\[ P_{\text{out}} = T \cdot \omega, \quad P_{\text{in}} = V \cdot I \]

Step 2: Detailed Explanation:
For an electric motor:
The electrical power input supplied to the terminals is given by:
\[ P_{\text{in}} = V \times I \]
where \(V\) is terminal voltage and \(I\) is current.
The useful mechanical power output delivered at the shaft is given by:
\[ P_{\text{out}} = T \times \omega \]
where \(T\) is the shaft torque and \(\omega\) is the angular velocity of rotation.
Taking the ratio of output power to input power:
\[ \eta = \frac{T \omega}{V I} \]

Step 3: Final Answer:
Therefore, the efficiency of an electric motor is represented as \(\frac{T \omega}{V I}\), matching option (A).