Two 2.0Ω resistors can be combined circuit to give an overall resistance of

Analyze the question: We have two identical 2.0 Ω resistors. We need to find the overall resistances possible when we connect them in a circuit. With only two resistors, there are two basic ways: series or parallel.

Concept:

• Series: R = R₁ + R₂
• Parallel: R = (R₁ × R₂)/(R₁ + R₂)

Solution:

Series: R = 2.0 + 2.0 = 4.0 Ω

Parallel: R = (2.0 × 2.0)/(2.0 + 2.0) = 4/4 = 1.0 Ω

So the two resistors can give either 1.0 Ω (parallel) or 4.0 Ω (series).

Checking the options:

• A and B: say "only", so they are too restrictive.
• C: includes 0.5 Ω, which is not possible with two 2.0 Ω resistors (0.5 Ω would need four 2.0 Ω resistors in parallel).
• D: either 1.0 Ω or 4.0 Ω, which matches our working.
• E: includes 0.5 Ω, which is not possible.

Tip: For two identical resistors of value R, remember the results are 2R (series) and R/2 (parallel). Here that gives 4 Ω and 1 Ω. Always check whether an option includes a value that would need more resistors than the question provides.