Question

For the following circuit: Find the currents i_a and i_b Find the voltage v_0 Find the power dissipated in each resistor Find the power generated by the 50V power source

Answer 1

a) R_1 = 20 times 80/20 + 80 = 1.6 ohm R_eq = 4 + 1.6 = 5.6 ohm i = 50/5.6 = 8.93 A Potential at 4 ohm is V_1 = iR = 8.93 times 4 = 35.72 Potential at 1.6 ohm is V_2 = iR = 8.93 times 1.6 = 14.288 Current through 20 ohm is i_a = V_2/R = 14.288/20 = 0.7144 A Current through 80 ohm is i_b = V_2/R = 14.288/80 = 0.1786 A b) potential V_0 = 14.288 V \r\n c) At 4 ohm P = i^2 R = (8.93)^2 times 4 = 318.98 W At 20 ohm P = i_a^2 R = (0.7144)^2 times 20 = 10.21 W At 80 ohm P = i_b^2 R = (0.1786)^2 times 80 = 2.55 W d) P = V I = 50 times 8.93 = 446.5