Question

The unit of specific resistance is
A.\[ohm-metr{{e}^{2}}\]
B. \[ohm\]
C. \[ohm-metre\]
D. ohm per metre

Answer 1

Hint: The SI unit of any quantity can be defined as the modern form of the metric system. It is the only system of measurement with an official status in nearly every country in the world. We can solve this question by substituting the dimensions of all the quantities in the formula for specific resistance which is given by
\[\rho =\dfrac{RA}{L}\]

Complete step-by-step answer:
Specific resistance is defined as the resistance offered per unit length and unit cross-sectional area when a known amount of voltage is applied. It can also be defined as the resistance offered by a wire of unit length and unit cross sectional area.
This can be mathematically represented as follows:
\[\rho =\dfrac{RA}{L}\]
Where,
⍴ is the specific resistance
R is the resistance of the given wire
A is the cross-sectional area of the given wire
L is length of the given material
Now, we know the units of resistance cross-sectional area and length are \[ohm\], \[metr{{e}^{2}}\] and meter respectively. So, substituting these values in the given formula we get.
 \[\rho =\dfrac{ohm\times metr{{e}^{2}}}{metre}\]
\[\rho =ohm\times metre\]
Hence, the correct answer is \[\rho =ohm\times metre\] which is option C.

Note: The resistance is an effect of a resistor which restricts the flow of electrons in a conducting material, that is, the resistor restricts the flow of current in a conductor. Specific resistance is also given by the reciprocal of specific conductance, which is defined as a measure of the ability of a material to conduct electricity. The symbolic representation of specific conductance is K.