A d.c motor has internal resistance 4 ohms . It is operated at 220 volts and draws 5 ampere current . The useful mechanical power developed is :-

Options

A. 550 W
B. 100 W
C. 1100 W
D. 1000 W

Answer

To solve the problem step by step, we will calculate the useful mechanical power developed by the DC motor.

### Step 1: Calculate the total power consumed by the motor and its internal resistance.

The formula for power (P) is given by:
\[ P = V \times I \]
Where:
- \( V \) is the voltage (220 volts)
- \( I \) is the current (5 amperes)

Substituting the values:
\[ P_{\text{total}} = 220 \, \text{V} \times 5 \, \text{A} = 1100 \, \text{W} \]

### Step 2: Calculate the power wasted due to the internal resistance.

The power wasted (P₀) in the internal resistance can be calculated using the formula:
\[ P_0 = I^2 \times R \]
Where:
- \( I \) is the current (5 amperes)
- \( R \) is the internal resistance (4 ohms)

Substituting the values:
\[ P_0 = (5 \, \text{A})^2 \times 4 \, \Omega = 25 \times 4 = 100 \, \text{W} \]

### Step 3: Calculate the useful mechanical power developed by the motor.

The useful mechanical power (P') developed by the motor can be found by subtracting the wasted power from the total power consumed:
\[ P' = P_{\text{total}} - P_0 \]

Substituting the values:
\[ P' = 1100 \, \text{W} - 100 \, \text{W} = 1000 \, \text{W} \]

### Final Answer:
The useful mechanical power developed by the motor is **1000 Watts**.

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