Two resistors R1 and R2 arranged in parallel combination in an electrical closed circuit are made of the same material and of same thickness. If the length of R2 is twice the length of R1, then the total resistance R satisfies
- A.3R = 2R1
- B.3R = 2R2
- C.2R = 3R1
- D.2R = 3R2
Correct answer
Explanation
The correct answer is A, 3R = 2R1. Since both wires have the same material and thickness, resistance is proportional to length, so R2 = 2R1, and the parallel combination works out to R = 2R1/3. The resistance of a wire is R = ρL/A, where ρ is the resistivity of the material, L the length and A the area of cross-section. With ρ and A the same for both, doubling the length doubles the resistance. For two resistors in parallel, R = R1R2/(R1 + R2). Putting R2 = 2R1 gives R = 2R1²/3R1 = 2R1/3, so 3R = 2R1. Option B is wrong because 3R equals R2, not 2R2. Option C is wrong because 2R = 3R1 would make the total larger than R1, while a parallel combination is always smaller than its smallest resistor. Option D is wrong for the same reason; it would make R even larger. Exam tip: in parallel, the total resistance is less than the smallest one; for wires of the same material and thickness, R is proportional to length.
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