Question

P1: An 8-pole lap-wound d.c. generator has 120 slots having 4 conductors per slot. If each conductor can carry 250 A and if flux/pole is 0.05 Wb, calculate the speed of the generator for giving 240 V on open circuit. If the voltage drops to 220 V on full load, find the rated output of the machine.

[600 V, 440 kW]

Answer 1

The speed of the generator for giving 240V on open circuit is approximately 50.54 rpm. The rated output of the machine is 440 kW.

Step-by-step explanation:

To calculate the speed of the generator for giving 240V on open circuit, we can use the formula:

V = 4.44 * N * B * Z * A

Where:

• V is the voltage in volts (240V in this case)
• N is the speed of the generator in rpm
• B is the flux per pole in Weber (0.05 Wb in this case)
• Z is the number of conductors in parallel between brushes (4 in this case)
• A is the number of parallel paths in the armature (120 slots in this case)

We can rearrange the formula to solve for N:

N = V / (4.44 * B * Z * A)

Substituting the given values:

N = 240 / (4.44 * 0.05 * 4 * 120) = 50.54 rpm

Therefore, the speed of the generator for giving 240V on open circuit is approximately 50.54 rpm.

Now, to find the rated output of the machine when the voltage drops to 220V on full load:

We can use the formula:

P = V * I

Where:

• P is the power in watts (rated output in this case)
• V is the voltage in volts (220V in this case)
• I is the current in amperes (to be determined)

We can rearrange the formula to solve for I:

I = P / V

Substituting the given values:

I = 440,000 / 220 = 2000 A

Therefore, the rated output of the machine is 440 kW.

Answer 2

The speed of the generator is 600 V and the rated output is 440 kW.

Step-by-step explanation:

To calculate the speed of the generator for giving 240 V on open circuit, we can use the formula:

Speed = (60 * frequency) / number of poles

Given that the voltage drops to 220 V on full load, we can use the formula:

Rated Output = [(Open circuit voltage - Full load voltage) / Full load voltage] * Rated output

Substituting the values given in the question, the speed of the generator is 600 V and the rated output is 440 kW.