How are imaginary numbersused in electrical engineering?
Imaginary numbers are used in electrical engineering because complex numbers are
an integral part of electrical problems. In fact, there are often more imaginary num-
bers in electrical engineering problems than there are real numbers. This is because a
complex number is a pair of numbers in which one number is real, the other imagi-
nary (or a real number multiplied by the value i,defined as the square root of 1; for
more information about imaginary numbers, see “Math Basics”).
For instance, we know electricity flows through an electrical circuit component
such as a light bulb. The bulb actually resists the flow of some electricity by doing
work—or shining—thus, the current is real and measured by a current meter. But if
the current can’t flow through a device, the current becomes imaginary. For example,
a capacitor is two pieces of metal that do not touch; therefore, if one adds a voltage, no
real current can flow through it.Is math used to describe the strength of materials?
Materials science is also a major part of engineering, and includes a great deal of
mathematics. For example, engineers need to know how materials stand up to stress
and strain from the pressure of either a structure or overlying materials. A basic
340 understanding of how structures respond to the action of forces and how these forces
How is mathematics used to determine
resistor values in an electrical network?E
lectrical engineers who deal with systems and circuit theory need to know
the terms and functions of the basic circuit element—resistor, capacitor, and
inductor—in terms of current-voltage associations determined by impedance
(obstruction). Complex numbers, calculus, and Laplace transforms (see above)
are all mathematical concepts used to understand circuit theory.The best way to understand the basics are through the following simple
equations:
Resistor—Voltage current (I) times resistance (R), or V IR.
Capacitor—Voltage the square root of 1 (j, often called i,or an imagi-
nary number) times frequency (w) times the capacitance (C)—all times the cur-
rent (I), or V (jwC)I;
Inductor—Voltage equals the current divided by the square root of 1 (j),
times frequency (w), times inductance (L), or V I/(jwL).