A dc machine tested at a constant speed of 1200 rpm had an induced voltage of200 V at a field current of 3 A. The armature resistance is 0.3 Ω and the fieldresistance is RF = 50 Ω. When operated at 1500 rpm the motor developed a powerof 2500 W and IF = 2.5 A. Find the developed torque Tdev, armature current IAand the voltage VT applied to the armature circuit

To find the developed torque Tdev, armature current IA, and the voltage VT applied to the armature circuit, we can follow these steps:

Step 1: Calculate the back EMF (Eb) at 1200 rpm. The back EMF (Eb) can be calculated using the formula: Eb = VT - IA * RA where VT is the total voltage applied to the armature circuit and RA is the armature resistance.

Given: Induced voltage (Eb) = 200 V Field current (IF) = 3 A Armature resistance (RA) = 0.3 Ω

Substituting the given values into the formula, we get: 200 V = VT - 3 A * 0.3 Ω

Simplifying the equation, we have: 200 V = VT - 0.9 V VT = 200 V + 0.9 V VT = 200.9 V

Therefore, the voltage VT applied to the armature circuit at 1200 rpm is 200.9 V.

Step 2: Calculate the developed torque (Tdev) at 1500 rpm. The developed torque (Tdev) can be calculated using the formula: Tdev = (Pdev * 60) / (2 * π * n) where Pdev is the developed power and n is the speed in revolutions per minute (rpm).

Given: Developed power (Pdev) = 2500 W Speed (n) = 1500 rpm

Substituting the given values into the formula, we get: Tdev = (2500 W * 60) / (2 * π * 1500 rpm)

Simplifying the equation, we have: Tdev = 0.0796 Nm

Therefore, the developed torque Tdev at 1500 rpm is 0.0796 Nm.

Step 3: Calculate the armature current (IA) at 1500 rpm. The armature current (IA) can be calculated using the formula: IA = (VT - Eb) / RA

Given: Voltage VT = 200.9 V (calculated in Step 1) Back EMF Eb = 200 V (given) Armature resistance RA = 0.3 Ω (given)

Substituting the given values into the formula, we get: IA = (200.9 V - 200 V) / 0.3 Ω

Simplifying the equation, we have: IA = 0.3 A

Therefore, the armature current IA at 1500 rpm is 0.3 A.