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 $\rho \rightarrow$ Resistivity
- Its S.I unit is Volt $/ A m p$ or ohm $(\Omega)$
- 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{aligned}
& \quad R=\rho \frac{l}{A} \\
& \text { As } \quad \rho=\frac{m}{n e^2 \tau} \\
& \text { And } \\
& \text { So } R \alpha \frac{1}{\tau}
\end{aligned}
$

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

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

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

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

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\left(1+\alpha\left(T-T_o\right)\right)
$

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

• Resistivity increases with impurity and mechanical stress.