UPSC Prelims 2001 Q100: Science & Technology – Physics
Two wires have their lengths, diameters and resistivities, all in the ratio of 1 :
2. If the resistance of the thinner wire is 10 ohms, the resistance of the thicker wire is
- (a) 10 ohms
- (b) 5 ohms
- (c) 20 ohms
- (d) 40 ohms
Answer: (a) 10 ohms
Explanation
Resistance of the thicker wire
| Quantity | Working |
|---|---|
| Given | Lengths, diameters and resistivities of the two wires are in the ratio 1 : 2; thinner wire = 10 ohms |
| Formula | R = ρ L / A, and A ∝ d² |
| Ratio for the thicker wire | ρ × 2, L × 2, A × 4 → R × (2 × 2) / 4 = × 1 |
| Resistance of the thicker wire | 10 ohms |
Given: two wires with lengths, diameters and resistivities in the ratio 1 : 2, and the thinner wire's resistance is 10 ohms. Resistance R = ρL/A. For the thicker wire, resistivity and length each double, raising R by 4 times, but the doubled diameter makes the area 4 times larger. The effects cancel, so its resistance is also 10 ohms.
Answer: (a) 10 ohms.
Why each option is right or wrong
- (a) CORRECT. The doubled ρ and L are cancelled by four times the area.
- (b) Incorrect. 5 ohms would need the area effect to be twice the others.
- (c) Incorrect. 20 ohms ignores that area grows with the square of diameter.
- (d) Incorrect. 40 ohms ignores the change in area altogether.
Key point
Resistance rises with length and resistivity, falls with area; area goes as the square of the diameter.
Remember
R = ρL/A; doubling ρ, L and d leaves R unchanged.
Common mistakes
- Treating area as proportional to diameter, not diameter squared.
- Forgetting resistivity also doubles.
- Multiplying all three ratios without dividing by area.
Exam tip
Write R = ρL/A and put the ratios in one at a time.
Sources
- NCERT Class X — Science, chapter 'Electricity' (resistivity)
- NCERT Class XII — Physics Part I, chapter 'Current Electricity'