What is the dimensional formula of Inductance?

• A). [M L² T⁻² A⁻²]
• B). [M L² T¹ A⁻²]
• C). [M L² T⁻¹ A⁻²]
• D). [M L² T⁻² A⁻¹]

Inductance is a property of an electrical circuit that quantifies how much voltage is induced in a circuit due to a change in current. The dimensional formula for inductance can be derived from its definition and the relationship between voltage, current, and time.

Dimensional Analysis of Inductance

The formula for inductance (L) is given by:

• Voltage (V) = Inductance (L) × Rate of change of current (dI/dt)

From Ohm's law, we know that:

• Voltage (V) = Current (I) × Resistance (R)

Resistance has the dimensional formula [M L² T⁻³ A⁻²]. Therefore, we can express voltage in terms of its dimensions:

• [V] = [M L² T⁻³ A⁻²] × [I] = [M L² T⁻³ A⁻¹]

Now, considering the rate of change of current (dI/dt), its dimensional formula is:

• [dI/dt] = [A T⁻¹]

Substituting these into the equation for voltage gives:

• [M L² T⁻³ A⁻¹] = [L] × [A T⁻¹]

Rearranging this to solve for the dimensional formula of inductance (L) results in:

• [L] = [M L² T⁻³ A⁻¹] × [A T] = [M L² T⁻² A⁻²]

Correct Answer

The dimensional formula of inductance is:

[M L² T⁻² A⁻²]

Thus, the correct option is A).