A conducting wire of length I and resistance R is cut into two eq

A conducting wire of length I and resistance R is cut into two eq
| A conducting wire of length I and resistance R is cut into two equal parts. The two parts are then connected in parallel. The resistance of the combination is

A. R/2

B. R/4

C. R

D. 2R

Please scroll down to see the correct answer and solution guide.

Right Answer is: B

SOLUTION

We know that

\(R = \frac{{\rho l}}{A}\)

Here R = resistance, ρ = resistivity, l = length, A = area

A conducting wire of length l and resistance R is cut into two equal parts that mean the new length of wire will be l/2 and according to the formula we know that R ∝ length

∴ 2 resistance connected in parallel with each value of resistance = R/2

∴ Equivalent resistance \( = {\rm{(}}\frac{R}{2}{\rm{||}}\frac{R}{2}{\rm{)}} = \frac{R}{4}\)

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