Advertisements
Advertisements
Question
Two identically built wires have the same length, but their radii are arranged in a 5 : 3 ratio. The resistance of the thicker wire, which is connected in series, is 12 Ω. Identify the total resistance of the combination.
Options
12 Ω
19 Ω
30 Ω
32 Ω
Advertisements
Solution
32 Ω
Explanation:
Resistance is inversely proportional to the square of the radius.
`R ∝ 1/r^2`
Thicker : Thinner radius = 5 : 3
`R_"think"/R_"thin" = 3^2/5^2`
`R_"think"/R_"thin" = 9/25`
Given, Rthink = 12 Ω
`R_"thin" = 12 xx 25/9`
= 33.3 Ω
Total resistance in series:
R = 12 + 33.3
= 45.3 Ω
Notes
The textbook answer key gives option (d) 32 Ω. However, using the standard formula `R ∝ 1/r^2` the calculated resistance is 45.3 Ω. This indicates a likely printing or calculation error in the textbook question or options or its answer key.
