Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 296

11.7.12 i nduCtanCe
To this point, we have learned the following key points about magnetic fields:

• A ield of force exists around a wire carrying a current.
• This ield has the form of concentric circles around the wire in planes perpendicular to the
wire, with the wire at the center of the circles.
• The strength of the ield depends on the current. Large currents produce large ields; small
currents produce small fields.
• When lines of force cut across a conductor, a voltage is induced in the conductor.

Moreover, we have studied circuits that have been resistive (i.e., resistors presented the only opposition
to current flow). Two other phenomena— inductance and capacitance —exist in DC circuits to some
extent, but they are major players in AC circuits. Both inductance and capacitance present a kind of
opposition to current flow that is called reactance . (Other than this brief introduction to capacitance
and reactance, we do not discuss these two electrical properties in detail in this text; instead, our focus
is on the basics, covering only those electrical properties important to water/wastewater operators.)
Inductance is the characteristic of an electrical circuit that makes itself evident by opposing the
starting, stopping, or changing of current flow. A simple analogy can be used to explain inductance.
We are all familiar with how difficult it is to push a heavy load (such as a cart full of heavy items).
It takes more work to start the load moving than it does to keep it moving. This is because the load
possesses the property of inertia . Inertia is the characteristic of mass that opposes a change in
velocity; it can hinder us in some ways and help us in others. Inductance exhibits the same effect
on current in an electric circuit as inertia does on velocity of a mechanical object. The effects of
inductance are sometimes desirable and sometimes undesirable.

Note: Simply put, inductance is the characteristic of an electrical conductor that opposes a change
in current flow.

Inductance is the property of an electric circuit that opposes any change in the current passing
through that circuit, so, if the current increases, a self-induced voltage opposes this change and
delays the increase. On the other hand, if the current decreases, a self-induced voltage tends to aid
(or prolong) the current flow, delaying the decrease. Thus, current can neither increase nor decrease
as quickly in an inductive circuit as it can in a purely resistive circuit. In AC circuits, this effect
becomes very important because it affects the phase relationships between voltage and current.
Earlier, we learned that voltages (or currents) could be out of phase if they are induced in separate
armatures of an alternator. In that case, the voltage and current generated by each armature were in
phase. When inductance is a factor in a circuit, the voltage and current generated by the same arma-
ture are out of phase. We will examine these phase relationships later. Our objective in this chapter
is to understand the nature and effects of inductance in an electric circuit.
The unit for measuring inductance ( L ) is the henry (named for the American physicist Joseph
Henry), which is abbreviated as h. Figure 11.62 shows the schematic symbol for an inductor. An induc-
tor has an inductance of 1 henry if an emf of 1 volt is induced in the inductor when the current through
the inductor is changing at the rate of 1 ampere per second. The relationships among the induced
voltage, inductance, and rate of change of current with respect to time can be stated mathematically as

EL I
t

= (11.57)

where
E = Induced emf (volts).
L = Inductance (henrys).
Δ I = Change in amperes occurring in Δ t seconds, where Δ (delta) means “a change in.”