Question

What is Ohm’s law? Explain how it is used to define the unit of resistance.

Answer 1

Hint: Recall the statement of Ohm’s law. Give the mathematical expression for Ohm’s law. Substitute the units of potential difference and electric current in this mathematical expression and define the unit of resistance of a conductor according to the unit expression for resistance.

Complete step by step solution:
The statement of Ohm’s law gives the relation between the current flowing through the current carrying conductor and the potential difference across the ends of the conductor.
The statement of Ohm’s law is as follows:
When the temperature and all the physical conditions are constant, the potential difference \[V\] across the ends of a current carrying conductor is directly proportional to the current \[I\] flowing through the conductor.
\[V \propto I\]
\[ \Rightarrow V = IR\]
Here, \[R\] is the constant of proportionality known as resistance of the conductor.
The unit of current is ampere (\[{\text{A}}\]) and the unit of the potential difference is volt (\[{\text{V}}\]).
Rearrange the above equation for the resistance of the current carrying conductor.
\[ \Rightarrow R = \dfrac{V}{I}\]
\[ \Rightarrow 1\,\Omega = \dfrac{{1\;{\text{V}}}}{{1\,{\text{A}}}}\]
The unit of the resistance is volt per ampere which is named after the German physicist Georg Simon Ohm.
When the potential difference of 1 volt is applied across the ends of a current carrying conductor, the current of 1 ampere flows through it. The resistance in such a conductor to the flow of the electric current is 1 ohm.

Note:
One can also define the unit of resistance in some other way but the definition given using Ohm’s law is the standard one. The unit of resistance of the current carrying conductor can also be defined in terms of the units of resistivity, length and cross-sectional area of the conductor. But here we have asked to define the unit of resistance using Ohm’s law.