For understanding the
reason, why current through and Inductor lags behind Voltage across the
Inductor, we will first go mathematically then we will understand the concept
analytically. Let us consider a purely inductive circuit as shown in figure
below.

As shown in the figure above,
an inductor of value L Henray is connected with an AC supply source V =
VmSinwt.

According to Kirchhoff’s loop law, the voltage
induced across the Inductor will be equal to the supply voltage and therefore we
can write as below.

VmSinwt = Voltage induced across Inductor

But induced emf in an
Inductor is Ldi/dt and therefore,

VmSinwt = Ldi/dt

⇒ Ldi
= VmSinwtdt

Integrating both sides, we
get

i = (Vm/wL)Coswt + C

where C is some constant.

Now, as the average value of
Coswt over one time period is zero and the supply voltage in our discussion in
sinusoidal, therefore we expect the current to be also sinusoidal. Therefore,
the value of constant C must be zero here in our case.

⇒ i =
(Vm/wL)Coswt

⇒ i =
(Vm/wL)Sin (wt – π/2)

Thus from the above
expression, we observe that the phase difference between the applied voltage V
= VmSinwt and current through Inductor i = (Vm/wL)Sin (wt – π/2) is π/2. This
means that the current through an inductor is lagging behind the applied
voltage V by an angle of 90°.

This was mathematical
calculation to show that current through an inductor is lagging the supply
voltage by an angle of 90°. But now we will discuss the same aspect but in
analytical way. For analytical discussion we will assume steady state
condition.

As we know that when a
current flows through a solenoid, a magnetic field is created by the solenoid
which remain confined inside the solenoid only. Now suppose, the current
through the solenoid is changing with time, that simply means that magnetic
flux will also change resulting into change in magnetic flux. As the coil of
solenoid is linking with this changing magnetic flux, an emf will be induced in
the solenoid in such a direction to oppose the cause in occurrence with Lenz’s
Law. Here the cause is current flowing through the solenoid, therefore the emf
will be induced in such a direction to oppose the flow of current. Here
solenoid is Inductor.

Let us consider steady state
where the supply voltage V is going positive from zero (point P in the figure
below). In this case, as the back emf of inductor will also be zero and
therefore the current flowing through the circuit will be maximum. Now as the supply
voltage increases in positive direction, back emf of inductor will also rise
but in opposite direction due to which the current flow through the circuit
will start decreasing and will become zero when the back emf of inductor
becomes maximum equal to the supply voltage as at that time supply voltage
become maximum positive (point Q in figure below). After that, the supply
voltage will start decreasing from it maximum value, but as the back emf of
inductor is maximum but opposite in direction, the current through the circuit
will change its direction. As the current in the circuit is flowing in opposite
direction, the back emf of inductor will start building up in opposite to the
direction of flow of current and hence net back emf of inductor will decrease
and will reach to zero when supply voltage reaches zero. At this point (R) maximum
current through the circuit will flow.

Thus we see that, it is the
generation of back emf in the inductor which forces the current flowing through
it to lag by applied voltage.

## No comments:

Post a Comment