Question

What is meant by resistance of a conductor? Name and define its S.I unit? List the factors on which the resistance of a conductor depends, how is the resistance of a wire affected if i) its length is doubled ii) its radius is doubled?

Answer 1

Resistance of a conductor simply defined as when flow of current is opposed or resisted in a material it is known as resistance and effect of length and the radius on conductor can be given by $R=\dfrac{\rho l}{A}$ where l is the length of the conductor and A is the area o0f the conductor.

Formula used:
$R=\dfrac{V}{I}$
$R=\dfrac{\rho l}{A}$

Complete step by step solution:
$\left( i \right)$ What is meant by resistance:-
Resistance is property of the conductor due to which it resists the flow of the electric current through it.

(ii) S.I unit of resistance is ‘ohm’ and it is denoted by the symbol $\left( \Omega \right)$

(iii) List the factor on which the resistance of a conductor depends.
$\bullet$ The temperature of the conductor
$\bullet$ Length of the conductor
$\bullet$ Material of the conductor
$\bullet$ Cross- sectional area of the conductor

(iv) How is the resistance affect if:
(i) Its length is doubled
(ii) Its radius is doubled

$\to$ We know that formula for resistance
$R=\dfrac{\rho l}{A}$
Where, $\rho$ = electrical resistivity
$l$ = length of the conductor
A = cross sectional area of the conductor

Hence if the length is doubled then
$\begin{aligned} & \Rightarrow {{R}_{1}}=\rho \dfrac{\left( 2l \right)}{A} \\\ & \therefore {{R}_{1}}=2\left( R \right) \\\ \end{aligned}$

So if the length of the resistance gets doubled then resistance also gets doubled,

Now when the radius is doubled then
$\begin{aligned} & \Rightarrow {{R}_{2}}=\dfrac{\rho l}{A} \\\ & \Rightarrow {{R}_{2}}=\dfrac{\rho l}{\pi \left( 2{{r}^{2}} \right)} \\\ & \therefore {{R}_{2}}=\dfrac{1}{4}\left( R \right) \\\ \end{aligned}$

So if the radius gets doubled then resistance will be ${{\dfrac{1}{4}}^{th}}$ of initial resistance.

Additional information:
Factors Affecting Resistivity:

1. Length of the conductor
2. The temperature of the conducting material
3. The cross-sectional area of the conductor
4. The material of the conductor

Note:
There is a difference between resistance and resistivity unlike resistance resistivity only depends upon temperature of the material. Which we have seen in the solution.