Q577
A copper wire of radius r and length l has a resistance of R. A second copper wire with radius 2r and length l is taken and the two wires are joined in a parallel combination. The resultant resistance of the parallel combination of the two wires will be
A.
5 R
B.
5 R/4
C.
4 R/5
D.
R/5
AnswerAnswer: Option D
Solution
Answer: Option D
Solution:
1st copper wire: R = pl/A = pl/ πr22ndcopper wire: R’ = p’l’/A’ = pl/(4 πr2) = R/4
If joined in parallel, (1/Req) = (1/R) + (1/R’)
= 1/R + 4/R
= 5/R
Req = R/5