Definition of Inductance:
Inductance is a fundamental property of an electrical conductor or circuit. It describes the tendency of the conductor to oppose any change in the electric current flowing through it.
When the current flowing through a conductor changes, it creates a changing magnetic field around it. According to Faraday's Law of Induction and Lenz's Law, this changing magnetic field induces a voltage (electromotive force or EMF) across the conductor. This induced voltage acts in a direction that opposes the original change in current.
In simpler terms: Inductance is like electrical inertia – it resists changes in current flow, just as mass resists changes in velocity.
Quantitatively:
It is defined as the ratio of the induced voltage (EMF) to the rate of change of current causing it:
E = -L (dI/dt)
Where:
E = induced voltage (EMF)
L = inductance
dI/dt = rate of change of current with respect to time
(The negative sign indicates the opposition, as per Lenz's Law).
* Alternatively, it can be defined as the ratio of the magnetic flux linkage (Φ) through the circuit to the current (I) producing the flux:
Φ = L * I
or L = Φ / I
Unit of Inductance:
The standard SI unit of inductance is the Henry.
Its symbol is H.
Definition of a Henry: One Henry (1 H) is the inductance of a circuit in which an electromotive force of one volt (1 V) is produced when the electric current through the circuit changes at a rate of one ampere per second (1 A/s).
Mathematically: 1 H = 1 V·s / A (one Volt-second per Ampere).
3. Dimensions of Inductance:
The dimensional formula expresses a physical quantity in terms of fundamental dimensions: Mass [M], Length [L], Time [T], and Electric Current [I] (or sometimes [A] for Ampere).
Using the formula E= L * (dI/dt) or L = V / (dI/dt):
Dimension of Voltage [V] = [Work / Charge] = [M L² T⁻²] / [I T] = [M L² T⁻³ I⁻¹]
Dimension of rate of change of current [dI/dt] = [I] / [T] = [I T⁻¹]
Therefore, the dimensions of Inductance [L] are:
[L] = [V] / [dI/dt]
[L] = [M L² T⁻³ I⁻¹] / [I T⁻¹]
[L] = M L² T⁻³⁺¹ I⁻¹⁻¹
[L] = M L² T⁻² I⁻²
So, the dimensional formula for inductance is [M L² T⁻² I⁻²] (or [M L² T⁻² A⁻²] if using A for Ampere).
Types of Inductance:
1. Self-Inductance (L): When a changing current in a coil induces an EMF in the same coil.
2. Mutual Inductance (M): When a changing current in one coil induces an EMF in a different nearby coil.
More topics :
Define Self Inductance and Expression for Coefficient of It
Expression For Self Inductance of a Solenoid - Param Himalaya