Dimensions of Resistance: The conductor’s resistance is the opposition offered by a conductor during the flow of change. Free electrons are accelerated and collide with positive ions whenever a potential difference is applied across a conductor, opposing their motion.
The resistance of the conductor refers to the opposition provided by ions. As a result, resistance is the property of a conductor that opposes the flow of current through it, and ohm is the unit of resistance.
Any physical quantity’s dimensional formula is the expression that represents how and which of the base quantities are included in that quantity.
For instance, it must be written by enclosing the symbols for base quantities with the appropriate power in square brackets ( ).
For example, the mass dimension formula is: (M)
We can say that the dimensional formula is the equation obtained by equating a physical quantity with its dimensional formula.
Resistance (R) = Voltage × Current-1 . . . . (1)
It is known that the formula of voltage (V) = Electric Field × Distance = (Force × Charge-1) × Distance
Now, the dimension formula of force can be written as M1 L1 T-2
Then, the dimensional formula of charge = current × time = I1 T1
Thus, the dimensional formula of voltage is written as (Force × Charge-1) × Distance
= (M1 L1 T-2) * (I1 T1)-1 * (L1) = (M1. L2. T-3. I-1)…..(2)
When placing equation (2) in equation (1), we get,
Resistance (R) = Voltage × Current-1
Or, R = (M1. L2. T-3. I-1) * (I)-1 = (M1. L2. T-3. I-2)
Thus, the resistance is dimensionally written as M. L2. T-3. I-2.
Dimensions of something like a physical quantity are the powers to which base quantities are raised to represent that quantity. In general, any physical quantity's dimensional formula is the expression that means how and which of the base quantities are included in that quantity.
M.L2. T-3. I-2 is the dimensional representation of resistance.
The resistance per unit length and cross-sectional area is known as resistivity. It's the property of a material that prevents the flow of charge or electric current. The ohmmeter is the unit of resistivity.