Question

A 250-V shunt-connected DC motor runs at 1500 rpm when it is not connected to any external load. When the motor is connected to an external load, it draws a line current of 40A. The motor has an armature resistance of 1 ? and a field circuit resistance of 100 ?. Assume that the rotational loss torque is 2 Nm and is independent of the speed (a) Find the line current of the motor when there is no external load. (b) Find the speed of the motor under the loaded condition. (c) Assuming that the field flux and current are linearly related. When the field circuit is reduced to 80 2, find the motor speed for the same external load as in (b) (Answers: 3.765 A, 1283 rpm, 1063 rpm)

Answer 1

Given, Supply voltage v = 250 v shunt field resistance, r_sh = 100 ohm armature resistance, r_a = 1 ohm speed when not connected to load, N_1 = 1500 rpm Rotational loss tourqe, T_rot = 2 Nm T_rot = k_e phi_a implies k_e phi = 2/I_a rightarrow circular 1 because E = v - I_a r_a k_e phi w_rn = 250 - I_a times 1 2/I_a times 1 2/I_a times 2 pi/60 = 250 - I_a 2/I_a times 2 pi times 1500/60 = 250 - I_a 100 pi/I_a = 250 - I_a implies 100 pi = 250 I_a - I_a^2 implies I_a^2 - 250 I_a + 100 pi = 0 implies I_a^2 - 250 I_a + 314 = 0 I_a = 248.73, 1.262 down arrow Not acceptable I_a = 1.262 A I_sh = v/r_sh = 250/100 = 2.5 A therefore Line current, I_L = I_a + I_sh = 1.262 + 2.5 I_L = 3.762 (b) when motor connected