Question

A piece of wire of resistance of 20 ohms is drawn out so that its length increases to twice its original length, calculate the resistance of the wire in the new situation

Answer 1

Hint:The resistance of wire dependency can be found out by using the relationship between the resistance and resistivity. It depends upon its length and also, upon the area of cross section. On the other hand, resistivity does not change with the change in length and area.

Complete step by step answer:
Resistance is a measure of the opposition to current flow in an electrical circuit
Given, initial resistance R= \[20\Omega \]
New length, l’= 2l
its area of cross-section becomes half so new area A’= A/2
using the formula, \[R=\dfrac{\rho l}{A}\]
\[\begin{align}
& R'=\dfrac{\rho l'}{A'} \\
&\Rightarrow R’ =\dfrac{\rho \times 2l}{\dfrac{A}{2}} \\
&\Rightarrow R’ =4\dfrac{\rho l}{A} \\
&\therefore R’ =4R \\
\end{align}\]
So, the new resistance becomes 4 times= 80\[\Omega \]
Additional Information:
Resistance is measured in ohms, symbolized by the Greek letter omega (Ω). It tells us how easily an electric current can flow through any material. If the resistance of the wire is high then the flow of current will be difficult through it. All materials resist current flow to some degree. There is a class of materials which offers zero resistance and they are called superconductors. When tolerance is indicated, the measured resistance value should be within the specified resistance range.

Note: We have used the dependency of the resistance on the length and area of cross-section. Ohm’s law gives us the relationship between the voltage applied across the ends of the conductor, the current flowing through it and the resistance.