What is the equivalent resistance of a 6 Ω resistor in parallel with a 3 Ω resistor?

What is the equivalent resistance of a 6 Ω resistor in parallel with a 3 Ω resistor?

• A. 3 Ω
• B. 6 Ω
• C. 2 Ω
• D. 1 Ω

Answer: (C)

When resistors are in parallel, the total resistance is found from the sum of their conductances, since they all share the same voltage and the current can split along multiple paths. The reciprocal rule is 1/R_eq = 1/R1 + 1/R2. Here, 1/R_eq = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2. So R_eq = 2 Ω. This checks out intuitively: the parallel combination provides more pathways for current, so the overall resistance Drops and is less than the smallest individual resistor (which is 3 Ω).

When resistors are in parallel, the total resistance is found from the sum of their conductances, since they all share the same voltage and the current can split along multiple paths. The reciprocal rule is 1/R_eq = 1/R1 + 1/R2.

Here, 1/R_eq = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2. So R_eq = 2 Ω.

This checks out intuitively: the parallel combination provides more pathways for current, so the overall resistance Drops and is less than the smallest individual resistor (which is 3 Ω).