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 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
1 answers
R/5
1st copper wire: R = pl/A = pl/ πr2
2ndcopper 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
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