Question

What is the change in resistance of a wire which is stretched triple its length?

Answer 1

Hint:The opposition to the flow of electrical current into an electrical circuit is known as resistance. As current flows through a cable, it produces resistance, is the resistance of wire.

Complete step by step answer:
It is necessary to keep in mind that a wire's resistance is inversely proportional to its area but directly proportional to its length. We can calculate the change in resistance by applying the formula,
\[R = \dfrac{{\rho L}}{A}\]
Where, \[\rho \] is the resistivity of the wire, $L$ is the length of the wire and $A$ is the cross sectional area of the wire.

That is, Resistance} =(Specific Resistivity Constant $\times$ Length of wire)} / Area of cross section of wire
\[R\alpha L\]
Therefore we can say that when the length of the wire is tripled then resistance will also become three times
\[R\alpha \dfrac{1}{A}\]
That is, the cross-section of the wire is cut to one third of its original cross-section, when it is extended to three times its original length. As a result from the above relationship, we find that the current resistance is 9 times that of the original resistance.

Note:Remember the formula \[R = \dfrac{{\rho L}}{A}\]. It is also important to note that resistance is directly proportional to length and inversely proportional to area. The longer a wire is, the more resistance it has because electrons must travel a longer path to get from one end to the other. The lower the resistance, the greater the cross sectional field, so the electrons have more space to pass through. This holds true regardless of how thick the wire is.