Question

What is meant by resistance of a conductor? Name and define its SI 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

The resistance of a conductor is the property by virtue of which it opposes the flow of charge s through it.

The more resistance the less is the charge I for a given potential difference.

It is equal to the ratio of potential difference applied across the conductor to the current flowing through it.

R = $\frac{V}{I}$

SI unit of resistance is Ohm.

I ohm = $\frac{I V}{1 ampere}$

           = $VA^{-1}$

Factors on which resistance of a conductor depends :

1) Length : The resistance of a conductor is directly proportional to its length.

R∝ l.

2) Area of cross section : The resistance R of a uniform conductor is inversely proportional to its area of cross section A,

R∝$\frac{1}{A}$

2) Nature of the material : The resistance of a conductor also depends on the nature of its material.

As per the question,

The resistance off a wire affected if :

(i) Length is doubled , resistance of wire will also doubled.

R∝ l

(ii) its radius is doubled, resistance of wire will be decrease four times.

R∝$\frac{1}{A}$

Answer 2

Resistance :

♪ Resistance of a conductor :

Mathematically, it is the ratio of Potential difference (V) applied across the ends of conductor to the current ( I ) flowing through it.

$\boxed{\mathsf{R\:=\:{\dfrac{V} {I}}}}$

♪ S. I. Unit :

S. I. Unit of resistance = $\mathsf{</strong><strong>\</strong><strong>O</strong><strong>mega</strong><strong>}$ ohm.

♪ Factors on which resistance of conductor depends :

By formula,

$\boxed{\mathsf{R\:=\:{\dfrac{{\rho}{L}}{A}}}}$

Resistance depends on :

1. L = length of conductor

2. A = Area of conductor

3. Nature of conductor

4. Temperature of the conductor.

♪ Affect :

( i ). If length is doubled,

By above relation, Length is directly proportional to Resistance.

So, when length is doubled, Resistance will get doubled or increase accordingly.

(ii ). If Radius is doubled,

Radius is related to Area of any circular or spherical body or portion or cross - section,

So, from above relation,

If radius will be doubled, then,

Area = $\mathsf{\pi{{r} ^{2}}}$

When radius get doubled,

Area = $\mathsf{\pi{{(2r)} ^{2}}}$

Area = $\mathsf{\pi{4{r} ^{2}}}$

Using above relation,

Resistance is inversely proportional to the Area of cross section,

Hence, Resistance will decrease 4 times.