In a parallel circuit, what is the total resistance of the 6 Ω and 3 Ω resistors in parallel?

In a parallel circuit, what is the total resistance of the 6 Ω and 3 Ω resistors in parallel?

• A. 2 Ω
• B. 3 Ω
• C. 6 Ω
• D. 9 Ω

Answer: (A)

In parallel circuits, the total resistance comes from adding the reciprocals of each resistor and then taking the reciprocal of that sum. This setup makes the overall opposition to current smaller than any individual resistor. Compute it step by step: 1/R_total = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2. So R_total = 2 Ω. This value is less than the smallest resistor (3 Ω), which is a hallmark of parallel combos. The other numbers would result from misapplying rules for series connections or focusing on a single resistor, not from the parallel arrangement. Thus the total resistance is 2 Ω.

In parallel circuits, the total resistance comes from adding the reciprocals of each resistor and then taking the reciprocal of that sum. This setup makes the overall opposition to current smaller than any individual resistor.

Compute it step by step: 1/R_total = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2. So R_total = 2 Ω.

This value is less than the smallest resistor (3 Ω), which is a hallmark of parallel combos. The other numbers would result from misapplying rules for series connections or focusing on a single resistor, not from the parallel arrangement. Thus the total resistance is 2 Ω.