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 use the following steps:

Step 1: Calculate the back EMF (Eb) at 1200 rpm: Given that the induced voltage (V) is 200 V at a field current (IF) of 3 A, we can use the formula: Eb = V + (IA * RA) where RA is the armature resistance. Substituting the given values, we get: Eb = 200 V + (3 A * 0.3 Ω) Eb = 200 V + 0.9 V Eb = 200.9 V

Step 2: Calculate the back EMF (Eb) at 1500 rpm: Since the motor is operated at 1500 rpm, we need to find the new back EMF. We can use the formula: Eb2 = Eb1 * (N2 / N1) where Eb1 is the back EMF at 1200 rpm, N1 is the initial speed, and N2 is the final speed. Substituting the given values, we get: Eb2 = 200.9 V * (1500 rpm / 1200 rpm) Eb2 = 251.125 V

Step 3: Calculate the developed torque (Tdev): The developed torque can be calculated using the formula: Tdev = (Eb - VT) / (IA + IF) where VT is the voltage applied to the armature circuit. Rearranging the formula, we get: Tdev = (Eb - VT) / (IA + IF) Substituting the given values, we have: 2500 W = (251.125 V - VT) / (IA + 2.5 A)

Step 4: Calculate the armature current (IA): To find the armature current (IA), we can rearrange the formula from Step 3: IA = (Eb - VT) / Tdev - IF Substituting the given values, we have: IA = (251.125 V - VT) / Tdev - 2.5 A

Step 5: Calculate the voltage applied to the armature circuit (VT): To find the voltage applied to the armature circuit (VT), we can rearrange the formula from Step 3: VT = Eb - (Tdev * (IA + IF)) Substituting the given values, we have: VT = 251.125 V - (Tdev * (IA + 2.5 A))

By following these steps and substituting the given values, you can find the developed torque (Tdev), armature current (IA), and the voltage applied to the armature circuit (VT).

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.