A shunt motor rotating at 1500 r/min is fed by a 120 V source. The line current is 51 A and the shunt field resistance is 120 ohm. If the armature resistance is 0.1 ohm, calculate the current in the armature.  

Explanation:

Shunt Motor Current Calculation

Definition: A shunt motor is a type of DC motor where the field windings are connected in parallel (or shunt) with the armature windings. It is widely used for applications requiring constant speed under varying load conditions.

Given Data:

• Motor speed = 1500 r/min
• Source voltage (V_s) = 120 V
• Line current (I_L) = 51 A
• Shunt field resistance (R_sh) = 120 Ω
• Armature resistance (R_a) = 0.1 Ω

Objective: To calculate the armature current (I_a).

Solution:

In a shunt motor, the line current (I_L) is the sum of the armature current (I_a) and the shunt field current (I_sh).

Step 1: Calculate the shunt field current (I_sh)

The shunt field current is given by Ohm's law:

I_sh = V_s / R_sh

Substitute the values:

I_sh = 120 V / 120 Ω

I_sh = 1 A

Step 2: Calculate the armature current (I_a)

The armature current is given by:

I_a = I_L - I_sh

Substitute the values:

I_a = 51 A - 1 A

I_a = 50 A

Conclusion:

The armature current in the motor is 50 A.

Additional Information

To further analyze the options, let’s evaluate why the other choices are incorrect:

Option Analysis:

Option 1: 1 A

This option is incorrect because 1 A is the shunt field current (I_sh), not the armature current (I_a). The armature current is calculated by subtracting the shunt field current from the line current, resulting in 50 A.

Option 2: 51 A

This option is incorrect because 51 A is the line current (I_L), which is the sum of the armature current and the shunt field current. The armature current alone is 50 A.

Option 3: 50 A

This is the correct answer. The armature current is calculated as the difference between the line current and the shunt field current, which is 50 A.

Option 4: 12 A

This option is incorrect and does not correspond to any calculation or parameter in this problem. It might be a distractor or an arbitrary value.

Conclusion:

In a shunt motor, the line current is the sum of the armature current and the shunt field current. By understanding this relationship and applying Ohm's law, the armature current is determined to be 50 A, making Option 3 the correct choice.