Resistance And Resistivity MCQ - Practice Questions with Answers

Resistance

• The resistance is known as the property of substance by virtue of which it opposes the flow of current through it.

• Formula-

For a conductor of resistivity $\rho$ having a length of a conductor= I
and Area of a crosssection of conductor= A
Then the resistance of a conductor is given as

$R=\rho \frac{l}{A}$

Where $\rho \to$ Resistivity
- Its S.I unit is Volt $/Amp$ or ohm $(\mathrm{\Omega })$
- Its Dimensions is $M{L}^2{T}^{-3}{A}^{-2}$
- Reciprocal of resistance is known as conductance.
- Resistance of a conductor depends on the following factors
1. Length -

$\text{ As }R=\rho \frac{l}{A}$

So Resistance of a conductor is directly proportional to its length
i.e. $R\alpha l$

2. Area of cross-section-

${}_{\mathrm{As}}R=\rho \frac{l}{A}$

Resistance of a conductor is inversely proportional to its area of cross-section

$\text{ i.e. }R\alpha \frac{1}{A}$

3. Material of the conductor-

${}_{\mathrm{As}}R=\rho \frac{l}{A}$

And For a conductor, if $\mathrm{n}=\mathrm{No}$. of free electrons per unit volume in the conductor, $\tau =$ relaxation time then the resistance of conductor

Then $\rho =\frac{m}{n{e}^2\tau }$
for different conductors n is different
And $\rho$ depends on n
So $R$ is also different.

 

4. Temperature-

$\begin{array}{rl}& R=\rho \frac{l}{A}\\ & \text{ As }\rho =\frac{m}{n{e}^2\tau }\\ & \text{ And }\\ & \text{ So }R\alpha \frac{1}{\tau }\end{array}$

And as temperature increases $\tau$ decrease
So as the temperature increases resistance increases
Temperature-dependent resistance is given by

$R_T=R_{T_0}[1+\alpha [T-T_0]]$

$R_T$ - Resistance at temperature $T$
$R_0$ - Resistance at temperature $T_o$
$\alpha$ - temperature coefficient of resistance

$\alpha =\frac{R_T-R_o}{R_o(T-T_o)}$

Where the value of $\alpha$ is different at different temperatures

 

• From Ohm's law 

                  V = IR

                   Where R =  Electric Resistance

1. Ohmic Substance: The substance which obeys Ohm's law are known as Ohmic substance. I-V graph is linear and the slope gives conductance which is reciprocal of resistance

2.   Non-ohmic substances

Those substances which don't obey Ohm's law are known as Non-ohmic or non-linear conductors.

For example gases, crystal rectifiers, etc. 

 

3.    Superconductor: For certain materials resistivity suddenly becomes zero below a certain temperature (critical temperature). The material in this state is called a superconductor.

In Superconductor, resistivity is zero

•  

 

   

Resistivity or Specific Resistance $(\rho )$
- As $R=\rho \frac{l}{A}$

If $\mathrm{l}=1\mathrm{m}$ and $\mathrm{A}=1{\mathrm{m}}^{\wedge }2$
Then $\mathrm{R}=\rho$
Resistivity is numerically equal to the resistance of a substance having a unit area of cross-section and unit length.
- Where $m$ is the mass, $n$ is the number of electrons per unit volume, $e$ is the charge of electron and $\tau$ is the relaxation time

Then $\rho =\frac{m}{n{e}^2\tau }$
- S.I Unit - Ohm.m
- Dimensions- $M{L}^3{T}^{-3}{A}^{-2}$

And as reciprocal of Resistivity is known as conductivity.
So the dimension of conductivity is $M^{-1}{L}^{-3}{T}^3{A}^2$

 

•  Resistivity is independent of the shape and size of the body as it is an intrinsic property of the substance.

The resistivity of a conductor depends on the following factors

1. Nature of the body-

${}_{\text{As }}\rho =\frac{m}{n{e}^2\tau }$

for different conductors n is different
And $\rho$ depends on n
$\mathrm{So}\rho$ is also different.

Temperature-dependent Resistivity :

$\rho ={\rho }_o(1+\alpha (T-T_o))$

$\rho :$ Resistivity at temperature T
${\rho }_{0:}$ Resistivity at the temperature $T_0$

• Resistivity increases with impurity and mechanical stress.