The dimension formula of potential difference is a physical quantity that represents the amount of work done per unit charge in moving a charge from one point to another point in an electric field. In other words, it is the difference in electric potential energy per unit charge between two points in an electric circuit. The dimension formula of potential difference is expressed in the SI unit of volts (V).

Formula for Potential Difference

The formula for potential difference is given by:

V = W/q

where V is the potential difference, W is the work done, and q is the charge. The potential difference is measured in volts (V), work done is measured in joules (J), and charge is measured in coulombs (C).

Dimensional Formula for Potential Difference

The dimensional formula for potential difference can be derived by substituting the dimensions of work and charge in the formula for potential difference. The dimension formula for work is given by:

[W] = [M][L]^2[T]^-2

where M represents mass, L represents length, and T represents time.

The dimension formula for charge is given by:

[q] = [I][T]

where I represents electric current and T represents time.

Substituting these dimension formulas in the formula for potential difference, we get:

[V] = [W]/[q]

[V] = [M][L]^2[T]^-2/[I][T]

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

Therefore, the dimension formula for potential difference is:

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

Conclusion

The dimension formula of potential difference represents the physical quantity that measures the amount of work done per unit charge in moving a charge from one point to another point in an electric field. The potential difference is measured in volts (V), and its dimensional formula is expressed in terms of mass, length, time, and electric current. Understanding the dimension formula of potential difference is essential in the study of electrical circuits and their applications.