Question

Example 2: Three resistors are connected in parallel as shown. A potential difference of 18.0 V is maintained between points a and b. (A) Calculate the equivalent resistance of the circuit 18.0 V 3.00 (2] 6.00 Ω| 9.00 Ω (B) Find the current in each resistor

Answer 1

(A) Since, all the resistors are connected in parallel combination: 1/Req = 1/R_1 + 1/R_2 + 1/R_3 = 1/3 + 1/6 + 1/9 therefore 1/Req = 6 + 3 + 2/18 = 11/18 therefore Req = 18/11 = 1.64 ohm (B) Since, all the resistors are connected in parallel Therefore potential across each resistor will be same. and equal to V. So, I_1 = V/R_1 = 18V/3 ohm = 6A I_2 = V/R_2 = 18V/6 ohm = 3A I_3 = V/R_3 = 18V/9 ohm = 2A c since, power (P) = I^2 R therefore P_1 = I^2_1 R_1 = (6)^2 (3) = 108W therefore P_2 = I^2_2 R_2 = (3)^2 (6) = 54W therefore P_3 = I^2_3 R_3 = (2)^2 (9) = 36W So, total power delivered = P_1 + P_2 + P_3 = 198W or, P_total = V^2/Req = (18)^2/1.64 = 198W