An AC (alternating current) circuit containing only a pure inductance operates based on the behavior of an inductor when subjected to an alternating voltage. Let's delve into the fundamental concepts of this type of circuit:
Pure Inductance:
A pure inductance circuit consists of an inductor and an AC voltage source. An inductor is a passive electrical component that resists changes in current flow through it. It stores energy in its magnetic field. The voltage across an inductor is proportional to the rate of change of current flowing through it. Mathematically, this relationship can be represented as:
=
V
L
=L
dt
di
Where:
V
L
is the voltage across the inductor.
L is the inductance of the inductor, measured in henries (H).
dt
di
represents the rate of change of current with respect to time.
Behavior in an AC Circuit:
When an AC voltage source is connected to a pure inductor, the voltage across the inductor alternates sinusoidally. As the voltage changes, the current through the inductor lags behind the voltage due to the inductor's inherent property of opposing changes in current. The relationship between the voltage and current in a pure inductance circuit can be described by the following equation:
=
sin
(
)
V=V
m
sin(ωt)
=
sin
(
−
)
I=I
m
sin(ωt−ϕ)
Where:
V is the instantaneous voltage across the inductor.
I is the instantaneous current flowing through the inductor.
V
m
is the peak voltage of the AC source.
I
m
is the peak current through the inductor.
ω is the angular frequency of the AC source (equal to
2
×
2π× frequency).
t is time.
ϕ is the phase angle between the voltage and current.
The phase angle
ϕ between the voltage and current is equal to 90 degrees in a pure inductance circuit. This means that the current lags behind the voltage by a quarter of a cycle.
Impedance of a Pure Inductance:
The impedance (
Z) of a pure inductance is a complex quantity that relates the voltage and current in an AC circuit. For a pure inductance, the impedance is given by:
=
Z
L
=jωL
Where:
Z
L
is the impedance of the inductor.
j is the imaginary unit (
2
=
−
1
j
2
=−1).
ω is the angular frequency.
L is the inductance.
In summary, a pure inductance circuit in an AC system exhibits a 90-degree phase shift between voltage and current. The impedance is solely determined by the inductance and frequency of the AC source. The circuit resists changes in current, causing the current to lag behind the voltage. This behavior has important implications in AC circuit analysis and design.