A 500 V shunt motor has armature resistance of .82 and field resistance of 200 Ω. Calculate the back EMF when the output is 8 kW at 80% efficiency.

Explanation:

Given the parameters of the 500 V shunt motor, we can calculate the back EMF (E_b) when the output power is 8 kW at an efficiency of 80%.

Step-by-Step Solution:

1. Determine the input power:

The output power (P_out) is given as 8 kW and the efficiency (η) is 80%.

Efficiency (η) = (P_out / P_in) × 100%

Rearranging the formula to find the input power (P_in):

P_in = P_out / (η / 100)

P_in = 8000 W / (80 / 100)

P_in = 8000 W / 0.8

P_in = 10000 W

2. Calculate the total current (I_total):

The input power to the motor is the product of the voltage (V) and the total current (I_total).

P_in = V × I_total

Rearranging the formula to find the total current (I_total):

I_total = P_in / V

I_total = 10000 W / 500 V

I_total = 20 A

3. Determine the field current (I_f):

The field resistance (R_f) is 200 Ω.

Using Ohm's Law:

I_f = V / R_f

I_f = 500 V / 200 Ω

I_f = 2.5 A

4. Calculate the armature current (I_a):

The total current is the sum of the armature current (I_a) and the field current (I_f):

I_total = I_a + I_f

Rearranging the formula to find the armature current (I_a):

I_a = I_total - I_f

I_a = 20 A - 2.5 A

I_a = 17.5 A

5. Calculate the voltage drop across the armature resistance (V_drop):

The armature resistance (R_a) is 0.82 Ω.

Using Ohm's Law:

V_drop = I_a × R_a

V_drop = 17.5 A × 0.82 Ω

V_drop = 14.35 V

6. Determine the back EMF (E_b):

The back EMF (E_b) is the input voltage minus the voltage drop across the armature resistance.

E_b = V - V_drop

E_b = 500 V - 14.35 V

E_b = 485.65 V

After rounding to the nearest whole number:

E_b = 486 V

Therefore, the back EMF when the output is 8 kW at 80% efficiency is 486 V.

Conclusion:

The correct option is Option 4: 486 V.

Important Information

To analyze the other options:

Option 1: 448.6 V

This value could be a miscalculation in the current or voltage drop. It is significantly lower than the correct back EMF of 486 V.

Option 2: 425 V

This value is also incorrect. It likely results from an error in calculating the input power or the voltage drop across the armature resistance.

Option 3: 465.8 V

While closer to the correct value, this option still does not match the correct back EMF of 486 V. It may be due to rounding errors or incorrect calculations of armature current or resistance.

Understanding the precise steps and calculations involved in determining the back EMF is crucial for ensuring accuracy in electrical engineering problems like this. This detailed solution showcases the importance of careful calculations and consideration of all relevant parameters.