Question

In the figure shown below, the battery has negligible internal resistance. (a) Compute the equivalent resistance of the network. (b) Find the current in each resistor. (c) Calculate the power consumption of each resistor.

Answer 1

Answer 2

2) a) 3 and 6 ohm are in parallel

R1 = 3*6 / (3 + 6) = 2 ohm

12 and 4 ohm are in parallel

R2 = 12*4 / (12 + 4) = 3 ohm

2 and 3 ohm are in series

R(equi) = R1 + R2 = 2 + 3 = 5 ohm

so the equivalent resistance is 5 ohm

b) current in the circuit = V/R(equi) = 60 / 5 = 12 A

Current in 3 ohm = 12*6 / (3 + 6) = 8 A

current in 6 ohm = 12 - 8 = 4A

current in 12 ohm = 12*4 / ( 12 + 4) = 3 A

current in 4 ohm = 12 - 3 = 9A

c) Power consumption in 3 ohm = I^2 R = 8^2 * 3 = 192W

Power Consumption in 6 ohm = 4^2*6 = 96 W

Power Consumption in 12 ohm = 12^2*3 = 432 W

Power Consumption in 4 ohm = 4^2 * 9 = 144 W