Question

The S.I. unit of specific resistance is?
A.)Ohm m-1
B.)Ohm m
C.)Ohm m2
D.)(Ohm)-1

Answer 1

Hint: Specific means known i.e. we are getting the result by applying known value of something. Resistance is simply an obstacle offered by anything w.r.t. parameters like length of wire, area, etc.

Complete step by step answer:
Units used to measure different quantities vary place to place. So to have a uniformity in units a system called ‘The International System of Units’ (abbreviated as SI) is used.
There are basic seven units defines in SI system:
Length - meter (m)
Time - second (s)
Amount of substance - mole (mole)
Electric current - ampere (A)
Temperature - kelvin (K)
Luminous intensity - candela (cd)
Mass - kilogram (kg)

Specific resistance is defined as the resistance of conductor of unit length and unit cross sectional area. It is denoted by $\rho$.

Ohm’s law: It states that current flowing through conductor is proportional to voltage applied across it.
$I\propto V$
$I=RV$
Where I is current flowing through conductor
     V is Voltage applied across conductor
     R is proportionality constant known as resistance
Therefore,
$R={\displaystyle \frac{I}{V}}$
This resistance is directly proportional to the length of the conductor and inversely proportional to the area of cross section of that conductor.

Therefore if l is length and A is area of cross section of conductor the resistance offered by that conductor is given by

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

Where $\rho$ is the proportionality constant known as specific resistance.
So,

$\rho ={\displaystyle \frac{RA}{l}}$
If all quantities are expressed in SI units then
$unitof\rho ={\displaystyle \frac{Ohm{m}^2}{m}}$
$unitof\rho =Ohmm$
Answer-(b)

Note: Do not get confused between resistance and specific resistance. The ratio of potential difference between two ends of a conductor to current is called resistance. It is not necessary to memorize units. Only understand the concept of specific resistance from that you can deduce the formula and units.