Question

If a wire of resistance R is stretched to double of its length, then new resistance will be :
(A) R/2
(B) 2R
(C) 4R
(D) 16R

Answer 1

Resistivity or resistance coefficient is a function of the material, which is why the substance resists the flow of current through it.
The strength of a wire made of that material is proportional to the length of the wire and inversely proportional to its cross-sectional area.
R= $\frac{\rho L}{A}$
Complete Step by step solution:
Resistance of wire is represented by
R= $\frac{\rho L}{A}$
While stretching a wire
(a) Volume of wire remains constant
(b) Wire length increases
(c) Cross section area decreases
(d) Wire Resistivity = constant
On stretching to double the length:
${{L}^{'}}$ =2L
${{A}^{'}}$ =$\frac{A}{2}$
R= $\frac{\rho {{L}^{'}}}{{{A}^{'}}}$= $\frac{\rho 2L}{A/2}$=$\frac{4\rho L}{A}$=4R
We observed that new resistance is 4 times of original resistance
C is the correct option

Note:
For a longer wire, the electrical resistance of a wire would be expected to be greater, for a wire of a wider cross sectional area less, and it would be expected to depend on the material from which the wire is produced.
The direction travelled by the electrons is also increased if the length of a material is increased. If electrons move for a long time, they collide further and, as a result, the amount of electrons moving through the substance reduces, thus reducing the current through the substance.
The current in any substance depends on amount of electrons per unit of time passing through a cross section of the substance. So, if any substance's cross section is wider, then the cross section can be crossed by more electrons. The passing of more electrons per unit time through a cross-section induces more current through the material.
More current implies less electrical resistance for fixed voltage and this relation is linear.