Two resistors 6 Ω and 3 Ω are in parallel across a 12 V source. What is the equivalent resistance and current from the source?

Two resistors 6 Ω and 3 Ω are in parallel across a 12 V source. What is the equivalent resistance and current from the source?

• A. Req = 3 Ω; I_source = 4 A
• B. Req = 1 Ω; I_source = 12 A
• C. Req = 6 Ω; I_source = 2 A
• D. Req = 2 Ω; I_source = 6 A

Answer: (D)

Parallel resistors share the same voltage, and their combined (equivalent) resistance is found from 1/Req = 1/R1 + 1/R2. For 6 Ω and 3 Ω, 1/Req = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2, so Req = 2 Ω. With a 12 V source, the total current is I = V / Req = 12 / 2 = 6 A. The current splits between the branches as I6Ω = 12/6 = 2 A and I3Ω = 12/3 = 4 A, which sum to the total 6 A. Other numbers would imply different equivalent resistances (for example, 3 Ω would give 4 A), but the parallel calculation gives 2 Ω and 6 A.

Parallel resistors share the same voltage, and their combined (equivalent) resistance is found from 1/Req = 1/R1 + 1/R2. For 6 Ω and 3 Ω, 1/Req = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2, so Req = 2 Ω. With a 12 V source, the total current is I = V / Req = 12 / 2 = 6 A. The current splits between the branches as I6Ω = 12/6 = 2 A and I3Ω = 12/3 = 4 A, which sum to the total 6 A. Other numbers would imply different equivalent resistances (for example, 3 Ω would give 4 A), but the parallel calculation gives 2 Ω and 6 A.