Final answer:
The input power of the DC generator is calculated to be 7750 W (7.75 kW) and the efficiency is found to be 85.16% by dividing the output power by the input power and multiplying the result by 100.
Step-by-step explanation:
To find the input power of a DC generator supplying a load, we start by calculating the output power which is given by multiplying the output current by the output voltage (Pout = IV). In this case, with a load of 30 A at an output voltage of 220 V, the output power is:
Pout = 30 A × 220 V = 6600 W (or 6.6 kW).
Next, we consider the losses to find the total input power, which is the sum of the output power and all the losses:
- Friction loss: 230 W
- Iron core loss: 145 W
- Field loss: 220 W
- Armature copper loss: 480 W
- Other stray losses: 75 W
Total losses = 230 W + 145 W + 220 W + 480 W + 75 W = 1150 W.
Then, input power (Pin) is the sum of the output power and total losses:
Pin = Pout + Total losses = 6600 W + 1150 W = 7750 W (or 7.75 kW).
To calculate the efficiency of the DC generator, use the efficiency formula:
Efficiency = (Output power/Input power) × 100 = (6600 W / 7750 W) × 100
Efficiency = 0.8516 × 100 = 85.16%