Dimensions of Resistance

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.

Dimensions 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.

Factors affecting resistance:

• Resistance is dependent on the length of the conductor.
• The conductor’s cross-sectional area.
• It is affected by the conductor’s material but is unaffected by the conductor’s geometry.
• This same resistance of the conductor is affected by its temperature.

Related Links:

Dimensions Of Coefficient Of Viscosity

Dimensions Of Current Density

Frequently Asked Questions (FAQs) on Dimensions of Resistance

What is the dimension formula?

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.

What is the dimensional formula of resistance?

M.L2. T-3. I-2 is the dimensional representation of resistance.

What is the dimensional analysis of resistivity?

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.