In a parallel circuit with R1 = 6 Ω and R2 = 3 Ω connected to a 12 V source, what is the total current and the current through each resistor?

In a parallel circuit with R1 = 6 Ω and R2 = 3 Ω connected to a 12 V source, what is the total current and the current through each resistor?

• A. Total current 4 A; I1 = 1 A through 6 Ω; I2 = 3 A through 3 Ω
• B. Total current 6 A; I1 = 2 A through 6 Ω; I2 = 4 A through 3 Ω
• C. Total current 8 A; I1 = 3 A through 6 Ω; I2 = 5 A through 3 Ω
• D. Total current 12 A; I1 = 6 A through 6 Ω; I2 = 6 A through 3 Ω

Answer: (B)

In a parallel circuit, the same voltage is across every branch, so each resistor draws a current given by I = V/R, and the total current is the sum of the branch currents. With a 12 V source across both resistors, the current through each branch is fixed: I1 = 12 V / 6 Ω = 2 A for the 6 Ω resistor, and I2 = 12 V / 3 Ω = 4 A for the 3 Ω resistor. The total current from the source is I_total = 2 A + 4 A = 6 A. You can also check by finding the equivalent resistance: R_eq = (6×3)/(6+3) = 2 Ω, and I_total = 12 V / 2 Ω = 6 A, which matches. So the correct description is a total current of 6 A, with 2 A through the 6 Ω resistor and 4 A through the 3 Ω resistor.

In a parallel circuit, the same voltage is across every branch, so each resistor draws a current given by I = V/R, and the total current is the sum of the branch currents. With a 12 V source across both resistors, the current through each branch is fixed: I1 = 12 V / 6 Ω = 2 A for the 6 Ω resistor, and I2 = 12 V / 3 Ω = 4 A for the 3 Ω resistor. The total current from the source is I_total = 2 A + 4 A = 6 A. You can also check by finding the equivalent resistance: R_eq = (6×3)/(6+3) = 2 Ω, and I_total = 12 V / 2 Ω = 6 A, which matches. So the correct description is a total current of 6 A, with 2 A through the 6 Ω resistor and 4 A through the 3 Ω resistor.