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
Step 1: Calculate the initial back EMF (E_b1). The back EMF of a DC shunt motor is given by the formula E_b = V - I_a R_a. Given: V = 300\, V I_a1 = 30\, A R_a = 0.5\, E_b1 = V - I_a1 R_a E_b1 = 300\, V - (30\, A)(0.5\, ) E_b1 = 300\, V - 15\, V E_b1 = 285\, V Step 2: Determine the armature current for the new speed. For a DC shunt motor, torque T is proportional to the product of flux and armature current I_a, i.e., T I_a. The problem states that the flux remains constant and the load torque T_L is kept constant. Therefore, the armature current must also remain constant. I_a2 = I_a1 = 30\, A Step 3: Calculate the back EMF (E_b2) at the new speed. The back EMF is also proportional to the product of flux and speed N, i.e., E_b N. Since the flux is constant, E_b N. We can write the ratio: E_b2E_b1 = (N_2)/(N_1) Given: N_1 = 1500\, r.p.m N_2 = 800\, r.p.m E_b2 = E_b1 ((N_2)/(N_1)) E_b2 = 285\, V (800\, r.p.m1500\, r.p.m) E_b2 = 285\, V ((8)/(15)) E_b2 = 19\, V × 8 E_b2 = 152\, V Step 4: Determine the total armature resistance required. Let R_ext be the external resistance added in series with the armature. The total armature circuit resistance will be R_a + R_ext. Using the back EMF formula for the new condition: E_b2 = V - I_a2 (R_a + R_ext) 152\, V = 300\, V - 30\, A (0.5\, + R_ext) Step 5: Solve for the external resistance R_ext. Rearrange the equation to solve for R_ext: 30\, A (0.5\, + R_ext) = 300\, V - 152\, V 30\, A (0.5\, + R_ext) = 148\, V 0.5\, + R_ext = 148\, V30\, A 0.5\, + R_ext = 4.9333... \, R_ext = 4.9333... \, - 0.5\, R_ext = 4.4333... \, Rounding to two decimal places: R_ext ≈ 4.43\, The value of resistance to be added in series with the armature is 4.43 .