Examining the Dimensional Formula of Resistance

When it comes to physics, understanding the dimensions of different quantities is crucial. In this context, we're going to delve into the dimensional formula of resistance.

The dimensional formula of resistance is represented as:

M ¹ L ² T ^-3 I ^-2

But what do these symbols mean? Let's break it down:

• M represents Mass
• I stands for Current
• L denotes Length
• T indicates Time

Detailed Derivation

To understand this better, let's look at the formula for Resistance (R), which is the product of Voltage and the reciprocal of Current. This can be represented as:

Resistance (R) = Voltage × Current ^-1

Voltage (V) can be expressed as the product of Electric Field and Distance, which is equivalent to Force multiplied by the reciprocal of Charge and then multiplied by Distance.

The dimensional formula of force is given by M ¹ L ¹ T ^-2 , whereas the dimensional formula of charge is the product of current and time, which is represented as I ¹ T ¹ .

Therefore, the dimensional formula of voltage, which is the product of Force and the reciprocal of Charge, and then multiplied by Distance, can be represented as:

[M ¹ L ¹ T ^-2 ] × [I ¹ T ¹ ] ^-1 × [L ¹ ] = [M ¹ L ² T ^-3 I ^-1 ]

By substituting this value in our original formula for resistance, we can conclude that:

Resistance (R) = [M ¹ L ² T ^-3 I ^-1 ] × [I] ^-1 = [M ¹ L ² T ^-3 I ^-2 ]

Hence, the dimensional representation of resistance is:

M L ² T ^-3 I ^-2

Explore Other Dimensional Formulas:

• Dimensions of Temperature
• Dimensions of Wavelength
• Dimensions of Boltzmann Constant
• Dimensions of Kinematic Viscosity
• Dimensions of Rotational Kinetic Energy