Question

A piece of wire of Résistance R is cut in to 5 equal parts and these parts are then
connected in parallel, if the equivalent resistance of these combination is 'x' then the
ratio of R/x?

Answer 1

$\bf \underline{Given}:$

▪ Resistance of wire: R

▪The piece of wire is cut into 5 equal parts.

▪If these (5 equal) parts are arranged in parallel,then the equal resistance becomes x

$\bf \underline{To \: find}:$

▪ The ratio of R/x

Resistance of each piece of wire after being cut into five equal parts =$\sf \dfrac{R}{5} \: \Omega$

We know that, in parallel combination :

$\sf \implies \dfrac{1}{x} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} + \dfrac{1}{R_4} + \dfrac{1}{R_5}$

$\sf \implies \dfrac{1}{x} = \dfrac{1}{\dfrac{R}{5} } + \dfrac{1}{\dfrac{R}{5} } + \dfrac{1}{\dfrac{R}{5} }+ \dfrac{1}{\dfrac{R}{5} }+\dfrac{1}{\dfrac{R}{5} }$

$\sf \implies \dfrac{1}{x} = \dfrac{5}{R} + \dfrac{5}{R}+\dfrac{5}{R}+\dfrac{5}{R}+\dfrac{5}{R}$

$\sf \implies \dfrac{1}{x} = \dfrac{25}{R}$

$\sf \implies \dfrac{R}{x} = 25$

So, the ratio of R/x is 25

Answer 2

▪ Resistance of wire: R

▪The piece of wire is cut into 5 equal parts.

▪If these (5 equal) parts are arranged in parallel,then the equal resistance becomes x

▪ The ratio of R/x

Resistance of each piece of wire after being cut into five equal parts =

We know that, in parallel combination :

So, the ratio of R/x is 25