This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Here are the calculations for the induction motor. Given: Frequency f = 50 Hz Number of poles P = 4 Rotor speed N_r = 1440 rev/min Total torque developed by the rotor T = 80 Nm Step 1: Calculate the synchronous speed (N_s). N_s = (120f)/(P) N_s = 120 × 50 Hz4 poles N_s = 1500 rev/min Step 2: Convert the synchronous speed to angular synchronous speed (_s). _s = (2 N_s)/(60) _s = 2 × 1500 rev/min60 s/min _s = 50 rad/s ≈ 157.08 rad/s --- 5.4.1 The total input (in kilowatts) to the rotor. The total input to the rotor is also known as the air gap power (P_ag). P_ag = T _s P_ag = 80 Nm × 50 rad/s P_ag = 4000 W P_ag ≈ 12566.37 W Convert to kilowatts: P_ag = (12566.37)/(1000) kW P_ag = 12.57 kW --- 5.4.2 The rotor copper loss in watts. Step 1: Calculate the slip (s). s = (N_s - N_r)/(N_s) s = 1500 rev/min - 1440 rev/min1500 rev/min s = (60)/(1500) s = 0.04 Step 2: Calculate the rotor copper loss (P_cu\_rotor). P_cu\_rotor = s × P_ag P_cu\_rotor = 0.04 × 12566.37 W P_cu\_rotor = 502.65 W Last free one today — make it count tomorrow, or type /upgrade for unlimited.