The **dimensional formula of inductance** is** [ML ^{2}T^{−2}A^{−2}]**. In this article, we will derive this dimensional formula of inductance.

**What is a Dimensional Formula?**

The dimensional formula is a way of expressing the physical quantity in terms of its fundamental dimensions. In physics, there are seven fundamental dimensions- Mass (M), Length (L), Time (T), Electric Current (A), Temperature(T), Amount of Substance (N), and Luminous Intensity (J).

Dimensional analysis is a powerful tool in physics and engineering for checking the consistency of equations and deriving relationships between physical quantities. If two physical quantities are added or equated, their dimensional formulas must be the same to be dimensionally consistent.

The formula or equation of that physical quantity must be known to derive the dimensional formula of quantity.

**Formula or Equation of Inductance**

Inductance is a property of an inductor or a coil that opposes changes in current passing through it. Inductance is denoted by the symbol “L” and is measured in units called henrys (H).

When the current flowing through an inductor changes, it induces an electromotive force (EMF) in the inductor. This induced EMF generates a magnetic field around the inductor. The inductance of a coil is a measure of the magnetic field produced in response to a change in current.

The mathematical relationship between inductance (L), induced EMF (e), and the rate of change of current (di/dt) is given by Faraday’s law of electromagnetic induction.

Where:

*e*is the induced electromotive force (EMF) in volts,*L*is the inductance in henrys,*di/dt*is the rate of change of current with respect to time.

Therefore, from equation (1), the inductance formula is.

**Dimensional Formula for Inductance**

The formula of inductance has two terms- EMF and rate of change of current. We will find the dimensional formula of these terms to get the dimensional formula of inductance.

**Dimensional formula of EMF(e)**

so,

Putting the fundamental value in the above expression,

**Dimensional formula of Rate of change of curre****nt(di/dt)**

The dimensional formula of current (I)) is given by:

The dimensional formula of time(t)) is given by:

The dimensional formula of the rate of change of current:

**Dimensional formula of Rate of inductance**

Putting the value of [e] and [di/dt] from equation(3) &(4) in equation(5),

The dimensional formula of inductance is.