Choose the correct answers to the questions from the given options. (Do not copy the questions, write the correct answers only.)
The correct formula to calculate the equivalent resistance of two resistors R₁ and R₂ when connected in parallel, is: (a) (R₁ + R₂) / (R₁R₂) (b) (R₁R₂) / (R₁ + R₂) (c) (R₁ − R₂) / (R₁R₂) (d) (R₁R₂) / (R₁ − R₂)
Topic: Equivalent resistance in parallel
Try it
Pick an option and check your answer. The full worked answer is below either way.
Answer
(b) For two resistors in parallel: 1/R = 1/R₁ + 1/R₂
Adding the fractions on the right: 1/R = (R₂ + R₁) ÷ (R₁R₂)
Inverting both sides: R = (R₁R₂) ÷ (R₁ + R₂)
Answer: (b) R₁R₂ / (R₁ + R₂)
Derive it rather than memorising it, and you will never pick the wrong option. Start from 1/R = 1/R₁ + 1/R₂, add the fractions, then turn the whole thing upside down — and it is that final inversion people forget, which is what makes option (a) look plausible.
Test the options with numbers if you are unsure. Take R₁ = R₂ = 2 Ω; two equal resistors in parallel must give 1 Ω. Option (b) gives 4 ÷ 4 = 1 ✓. Option (a) gives 4 ÷ 4 = 1 as well here, so try unequal values: R₁ = 6, R₂ = 3 should give 2 Ω. Option (b) gives 18 ÷ 9 = 2 ✓, option (a) gives 9 ÷ 18 = 0.5 ✗.
Options (c) and (d) both use R₁ − R₂, which cannot be right: if the two resistances were equal it would mean dividing by zero. This shortcut works for exactly TWO resistors; for three or more, go back to 1/R = 1/R₁ + 1/R₂ + 1/R₃.
For two resistors in parallel: 1/R = 1/R₁ + 1/R₂
Adding the fractions on the right: 1/R = (R₂ + R₁) ÷ (R₁R₂)
Inverting both sides: R = (R₁R₂) ÷ (R₁ + R₂)
Answer: (b) R₁R₂ / (R₁ + R₂)