Question

The resistance of a conducting wire X of length 1 m is 5 Ω. Calculate the resistance of the wire made by the same material whose length is 4 times and area of cross-section is 5 times that of wire X. (At same temperature ).

Please answer this with full explanation ✨✨☺️​

Answer 1

Given,

For a conducting wire X,

• R = 5 Ω
• l = 1 m
• a = ?

Another wire made by the same material whose length is 4 times and area of cross-section is 5 times that of wire X.

• L = 4 * l = 4 m
• A = 5 * a = 5a

To find :

The resistance of the other wire.

Solution

We know,

$\bigstar\ \sf{R=\rho \dfrac{l}{a} }$

For wire X,

$\sf{5=\rho \dfrac{1}{a} }$

For the other wire,

Let the resistance be R'. Then,

$\sf{R'=\rho \dfrac{4l}{5a} }\\\\\sf{\implies R'=\rho \dfrac{4}{5}\times \dfrac{l}{a} }\\\\\sf{\implies R'=\rho \dfrac{4}{5}\times \dfrac{1}{a} }\\\\\sf{\implies R'= \dfrac{4}{5}\times \rho \dfrac{1}{a} }\\\\\sf{\implies R'= \dfrac{4}{5}\times R }\\\\\sf{\implies R'= \dfrac{4}{5}\times 5 }\\\\\boxed{\sf{\implies R'=4\ \Omega}}$

Hence, the resistance of the wire made by the same material whose length is 4 times and area of cross-section is 5 times that of wire X is 4 Ω.