In a parallel circuit with R1 = 2 Ω, R2 = 4 Ω, R3 = 4 Ω connected to 12 V, what is the total current and the current through each resistor?

• A. I_total = 6 A; I1 = 3 A; I2 = 2 A; I3 = 2 A
• B. I_total = 12 A; I1 = 6 A; I2 = 3 A; I3 = 3 A
• C. I_total = 36 A; I1 = 12 A; I2 = 12 A; I3 = 12 A
• D. I_total = 10 A; I1 = 5 A; I2 = 5 A; I3 = 0 A

Answer: (B)

In a parallel circuit, the voltage across every resistor is the same as the source voltage, so each branch draws current according to I = V/R. With a 12 V supply, the currents are: for the 2 Ω resistor, I = 12/2 = 6 A; for each 4 Ω resistor, I = 12/4 = 3 A. Since currents in parallel add at the junctions, the total current is 6 A + 3 A + 3 A = 12 A. So the total current is 12 A, and the currents through the resistors are 6 A, 3 A, and 3 A, respectively.