A d.c. motor connected to a 240 V supply is developing 20 kW at a speed of \( 900 \mathrm{r} / \mathrm{min} \). Calculate the useful torque. [212 Nm]

To find the useful torque developed by the motor, we can use the formula that relates power (P), torque (T), and angular speed (ω): \[ P = T \times ω \] First, we need to convert the speed from revolutions per minute (r/min) to radians per second (rad/s): \[ ω = \frac{2\pi \times \text{speed in r/min}}{60} \] Substituting the given speed: \[ ω = \frac{2\pi \times 900}{60} = 94.2478 \, \text{rad/s} \] Now, we can rearrange the power equation to find the torque: \[ T = \frac{P}{ω} \] Substituting the known values: \[ T = \frac{20000 \, \text{W}}{94.2478 \, \text{rad/s}} \] Calculating this gives: \[ T \approx 212 \, \text{Nm} \] Thus, the useful torque developed by the motor is approximately 212 Nm.