SelfInductance
and Inductive Reactance
The property of selfinductance
is a particular form of electromagnetic induction. Self inductance
is defined as the induction of a voltage in a currentcarrying
wire when the current in the wire itself is changing. In the case
of selfinductance, the magnetic field created by a changing current
in the circuit itself induces a voltage in the same circuit. Therefore,
the voltage is selfinduced.
The term inductor is used to describe a circuit
element possessing the property of inductance and a coil of wire
is a very common inductor. In circuit diagrams, a coil or wire
is usually used to indicate an inductive component. Taking a closer
look at a coil will help understand the reason that a voltage
is induced in a wire carrying a changing current. The alternating
current running through the coil creates a magnetic field in and
around the coil that is increasing and decreasing as the current
changes. The magnetic field forms concentric loops that surround
the wire and join to form larger loops that surround the coil
as shown in the image below. When the current increases in one
loop the expanding magnetic field will cut across some or all
of the neighboring loops of wire, inducing a voltage in these
loops. This causes a voltage to be induced in the coil when the
current is changing.
By studying this image of a coil, it can be seen that the number
of turns in the coil will have an effect on the amount of voltage
that is induced into the circuit. Increasing the number of turns
or the rate of change of magnetic flux increases the amount of
induced voltage. Therefore, Faraday's Law must be modified
for a coil of wire and becomes the following.
Where:
VL = induced voltage in volts
N = number of turns in the coil
dø/dt = rate of change of magnetic flux in
webers/second
The equation simply states that the amount of induced voltage
(VL) is proportional to the number of turns
in the coil and the rate of change of the magnetic flux (dø/dt).
In other words, when the frequency of the flux is increased or
the number of turns in the coil is increased, the amount of induced
voltage will also increase.
In a circuit, it is much easier to measure current than it is
to measure magnetic flux, so the following equation can be used
to determine the induced voltage if the inductance and frequency
of the current are known. This equation can also be reorganized
to allow the inductance to be calculated when the amount of inducted
voltage can be determined and the current frequency is known.
Where:
VL = the induced voltage in volts
L = the value of inductance in henries
di/dt = the rate of change of current in amperes per second
Lenz's Law
Soon after Faraday proposed his law of induction, Heinrich Lenz
developed a rule for determining the direction of the induced
current in a loop. Basically, Lenz's law states that an induced
current has a direction such that its magnetic field opposes the
change in magnetic field that induced the current. This means
that the current induced in a conductor will oppose the change
in current that is causing the flux to change. Lenz's law is important
in understanding the property of inductive reactance, which is
one of the properties measured in eddy current testing.
Inductive Reactance
The reduction of current flow in a circuit due to induction
is called inductive reactance. By taking a closer
look at a coil of wire and applying Lenz's law, it can be seen
how inductance reduces the flow of current in the circuit. In
the image below, the direction of the primary current is shown
in red, and the magnetic field generated by the current
is shown in blue. The direction of
the magnetic field can be determined by taking your right hand
and pointing your thumb in the direction of the current. Your
fingers will then point in the direction of the magnetic field.
It can be seen that the magnetic field from one loop of the wire
will cut across the other loops in the coil and this will induce
current flow (shown in green) in
the circuit. According to Lenz's law, the induced current must
flow in the opposite direction of the primary current. The induced
current working against the primary current results in a reduction
of current flow in the circuit.
It should be noted that the inductive reactance will increase if
the number of winds in the coil is increased since the magnetic
field from one coil will have more coils to interact with.
Similarly to resistance, inductive reactance reduces the flow of current in a circuit. However, it
is possible to distinguish between resistance and inductive reactance
in a circuit by looking at the timing between the sine waves of
the voltage and current of the alternating current. In an AC circuit
that contains only resistive components, the voltage and the current
will be inphase, meaning that the peaks and valleys of their
sine waves will occur at the same time. When there is inductive
reactance present in the circuit, the phase of the current will
be shifted so that its peaks and valleys do not occur at the same
time as those of the voltage. This will be discussed in more detail
in the section on circuits.
