UPSC Prelims 2001 · General Studies
Question 100: Science and Technology
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
AnswerThe answer is (a).
Resistance R = rho x L / A, and the area A is proportional to the square of the diameter. Take the thinner wire as 1 for each quantity and the thicker as 2. Then R(thick) / R(thin) = (2 / 1) x (2 / 1) x (1 / 2)^2 = 1. So the thicker wire also has resistance 10 ohms: doubling the length and resistivity doubles resistance twice, while doubling the diameter quadruples the area and cuts resistance four times.
Why each option is right or wrong
- (a) Right: the ratio works out to 1, so 10 ohms.
- (b) 5 ohms would need the ratio of resistances to be 1 : 2, but it is 1 : 1.
- (c) 20 ohms would need the resistance to double, but the factors cancel.
- (d) 40 ohms would need a four-fold rise, which the ratios do not give.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2001, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.