Question

State and define the S.I. unit of resistance.

Answer 1

Hint: The given question is based on the concept of Ohm’s law. We will define the parameter resistance using Ohm’s law and will further continue with the explanation of the unit of the resistance using the formula of Ohm’s law.

Formula used: \[V=IR\]

Complete step by step answer:
Ohm’s law states that the voltage supplied to the circuit is directly proportional to the flow of current. The mathematical representation of the same is given as follows.
\[V\propto I\]
This proportionality constant is replaced by a parameter named the resistance of the circuit.
\[V=IR\]
Where R is the resistance offered by the circuit.
The resistance is defined as the opposition offered to the flow of current through the circuit.
The formula that relates the current, voltage and the resistance is given as follows. This relation is defined by Ohm’s law.
\[V=IR\]
Where V is the voltage, I is the current and R is the resistance.
The unit of the resistance is given as follows.
Firstly, we will represent the formula of Ohm’s law in terms of the resistance. So, we get,
\[R=\dfrac{V}{I}\]
The unit of the voltage is given as V, abbreviated as volts and the unit of the current is given as A, abbreviated as ampere. Now, represent the unit of the resistance in terms of the units of the voltage and current, so, we get,
\[R=\dfrac{V}{A}\]
Thus, the general unit of the resistance is volts per ampere.
The SI unit of the resistance is given a scientist name who defined the term resistance, that is, Ohm.
So, the SI unit of the resistance is the ohm, the symbol used to represent the same is \[\Omega \].
The definition of S.I. unit of the resistance: 1 ohm is the amount of resistance offered by the circuit when the voltage of 1 volt is applied across the circuit and the current of 1 ampere flows through it.

\[\therefore \] The SI unit of the resistance is 1 ohm (1 \[\Omega \]).

Note: This is a direct theoretical question. As the parameter resistance offered by the circuit is defined by Ohm’s law, thus, we have discussed the same first, continuing with the unit of the resistance. Whenever the definition of the unit is asked, equate the terms to unit values as above.