Final answer:
The duty ratio of the chopper for a 230 V, 1200 rpm, 15 A separately excited motor with an armature resistance of 1.2 ohms, operated under dynamic braking with chopper control, cannot be calculated exactly without additional information on the motor's torque-speed characteristics and the braking dynamics.
Step-by-step explanation:
To calculate the duty ratio of the chopper for a separately excited motor under dynamic braking with chopper control, we first determine the motor's electrical output power at the rated conditions. The electrical power output (Po) can be calculated as the product of the voltage (V) and the current (I), yielding 230 V × 15 A = 3450 W. Next, we calculate the power developed at 1200 rpm. Since power is proportional to torque (T) and speed (N), and the braking torque is 1.5 times the rated motor torque, we have Pdev = 1.5 × Po (1200/1000) due to the linear relationship between speed and torque for given power. As speed decreases to 1000 rpm, the power would be P1000 = 1.5 × 3450 W × (1200/1000).
Now, since the braking force is supplied by the chopper-controlled resistor (Rb), we can calculate the energy dissipated in Rb as Pb = I2 × Rb. However, the average power in the braking resistor during dynamic braking with chopper control will be Pavg = Pb × duty ratio (D). To maintain the braking power desired, we set Pavg equal to P1000.
a
Without the specifics of the motor's torque-speed characteristics and the exact method the motor handles dynamic braking, it is not possible to provide an exact duty ratio calculation.