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 calculate the useful torque produced by the DC motor, we can use the formula: \[ \text{Power} = \text{Torque} \times \text{Angular Speed} \] First, we need to convert the speed in revolutions per minute (r/min) to radians per second (rad/s): \[ \text{Angular Speed} = \frac{900 \, \text{rev/min} \times 2\pi \, \text{rad/rev}}{60 \, \text{s/min}} = 94.2478 \, \text{rad/s} \] Next, we rearrange the power formula to solve for torque: \[ \text{Torque} = \frac{\text{Power}}{\text{Angular Speed}} = \frac{20000 \, \text{W}}{94.2478 \, \text{rad/s}} \approx 212 \, \text{Nm} \] Thus, the useful torque developed by the motor is approximately \( 212 \, \text{Nm} \).