A copper wire of radius r and length 1 has a resistance of R. A second copper wire with radius 2r and length 1 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
5R
5/4 R
4/5 R
R/5
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CDS-1 – 2017
– For the second wire: The radius is 2r, and the length is l. So, R₂ = ρ * (l / π(2r)²) = ρ * (l / 4πr²) = (1/4) * [ρ * (l / πr²)] = R/4.
– When two resistors R₁ and R₂ are connected in parallel, the resultant resistance R_eq is given by 1/R_eq = 1/R₁ + 1/R₂ or R_eq = (R₁ * R₂) / (R₁ + R₂).
– Plugging in the values, R_eq = (R * (R/4)) / (R + R/4) = (R²/4) / (5R/4).
– R_eq = (R²/4) * (4/5R) = R/5.