A 12 V source across two resistors in parallel: 6 Ω and 3 Ω. Find branch currents and total current.

A 12 V source across two resistors in parallel: 6 Ω and 3 Ω. Find branch currents and total current.

• A. I6 = 2 A; I3 = 4 A; I_total = 6 A
• B. I6 = 1 A; I3 = 3 A; I_total = 4 A
• C. I6 = 3 A; I3 = 2 A; I_total = 5 A
• D. I6 = 2 A; I3 = 3 A; I_total = 5 A

Answer: (A)

In a parallel circuit, the supply voltage appears across every branch, and each branch current is found by Ohm’s law I = V/R. With 12 V across both resistors, the current through the 6 Ω branch is 12/6 = 2 A, and the current through the 3 Ω branch is 12/3 = 4 A. The total current is the sum of the branch currents: 2 A + 4 A = 6 A. (Equivalently, the equivalent resistance is (6*3)/(6+3) = 2 Ω, so I_total = 12/2 = 6 A.) So the currents are 2 A through the 6 Ω resistor, 4 A through the 3 Ω resistor, and 6 A total. Other sets of currents would not satisfy I = V/R for these resistors.

In a parallel circuit, the supply voltage appears across every branch, and each branch current is found by Ohm’s law I = V/R. With 12 V across both resistors, the current through the 6 Ω branch is 12/6 = 2 A, and the current through the 3 Ω branch is 12/3 = 4 A. The total current is the sum of the branch currents: 2 A + 4 A = 6 A. (Equivalently, the equivalent resistance is (6*3)/(6+3) = 2 Ω, so I_total = 12/2 = 6 A.) So the currents are 2 A through the 6 Ω resistor, 4 A through the 3 Ω resistor, and 6 A total. Other sets of currents would not satisfy I = V/R for these resistors.