VK5AJL - Mathematical Symbols

MATHEMATICAL AND OTHER SYMBOLS
AS USED ON THIS SITE

Some symbols are used to represent finite values such as Ω for ohms eg. 12Ω and others are used to represent unknown quantities eg. R for resistance. Some letters might be confused with various values eg. "I" is traditionally used for Current but might be confused with Inductance (generally L) or Impedance (generally Z). The letters or symbols used on this site, are listed here to prevent any such confusion.

Greek letters and other strange signs
Π
Symbol for the number PI or 3.1415927.... Π is often stated as being the ratio of circumference of a circle to the diameter and this is true but, strangely enough, this is not how it is calculated. A power series for 4 x arctan(-1) can be used ie. Π = 4 x (1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 ......)

Ω
Symbol used for a value in ohms usually referring to resistance or impedance. The letter R is often used in its place for resistance. (See also Z below for impedance.)

Ø
Used to represent an angle. On this site, angles are measured in radians. Expressed as radians, an angle is represented as the ratio of the circumference of an arc to its radius. In one cycle, the circumference is Π if the diamater is 1 so there are 2Π radians in one cycle since d=2r. Where it is desirable to express angles in degrees, the normal degrees designator is used ie. 90^o = Π/2 radians

ω
Symbol used for angular frequency in radians per second thus ω = 2Πf

∞
Infinity. There is no such quantity but, it can be argued, there is such a number, OR is that the other way around - who cares? This quantity may not actually occur in real circuits but the impedance of a parallel LC circuit using perfect components is mathematically infinite.

| |
A symbol for an unknown value enclosed in two vertical lines means the absolute value of the quantity thus |Z| is the absolute value of impedance and has no direction, +ve or -ve.

English letters including strangely written ones

j	√-1 or the square root of -1. This number has no meaning in the normal real numbers. There is no negative number with a real square root. This is why vector quantities containg a j component are called imaginary although complex is also often used and propably a better adjective. " i " is often used instead of " j ".
Z Z_C Z_L	Symbol used for impedance. For a capacitor, impedance is written as Z_C while for an inductor as Z_L. Impedance should not be confused with reactance. Impedance is a complex quantity with real and imaginary parts. For a capacitor, Z_C = - j / ωC while for an inductor, Z_L = j ω L. \|Z_L\| = \|X_L\| when Ø = Π/2 WHILE \|Z_C\| = \|X_C\| when Ø = -Π/2 AND Z=R when Ø = 0 (Ø is the phase angle between voltage and current.) Impedance is used for both single components or complex circuits ie -Π/2 < Ø < +Π/2
X X_C X_L	Symbol for reactance. For an inductor X_L = ωL and for a capacitor X_C = - 1/(ωC). Capacitive reactance is given as a -ve number because the current leads the voltage by Π/2 radians although the equation is often just written as X_C = 1/(ωC) as a short form of \|X_C\| = 1/(ωC) Reactance is usually a value associated with a single component. It doesn't make sense to use reatance when the phase angle is not +Π/2 or -Π/2.
R	Used to represent an unknown quantity of resistance. (See also Ω above.)
f	Frequency in cycles per second measured in Hz.
L	Used to represent inductance usually of an unknown quantity. Inductance is measured in Henries in which case H, or more commonly mH or μH, is used to represent a specific value.
C	Used to represent capacitance usually of an unknown quantity. Capacitance is measured in Farads in which case C, or more commonly μF, nF or pF, is used to represent a specific value.
I	Used to represent an unknown value of current. Current is measured in amps.
V	Many use E, EM or EMF to express Electro Motive Force. I prefer to simply use V to eliminate confusion with Electro Magnetic eg EM radiation. This site therefore uses V for both unknown and known quantities of volts.
W or P	An unknown quantity of power is usually expressed as "P" while a known quantity using "W" for watts. I have developed the, probably bad habit, of using W for both. This site will use "W" most of the time but "P" if I remember.

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Π	Symbol for the number PI or 3.1415927.... Π is often stated as being the ratio of circumference of a circle to the diameter and this is true but, strangely enough, this is not how it is calculated. A power series for 4 x arctan(-1) can be used ie. Π = 4 x (1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 ......)
Ω	Symbol used for a value in ohms usually referring to resistance or impedance. The letter R is often used in its place for resistance. (See also Z below for impedance.)
Ø	Used to represent an angle. On this site, angles are measured in radians. Expressed as radians, an angle is represented as the ratio of the circumference of an arc to its radius. In one cycle, the circumference is Π if the diamater is 1 so there are 2Π radians in one cycle since d=2r. Where it is desirable to express angles in degrees, the normal degrees designator is used ie. 90^o = Π/2 radians
ω	Symbol used for angular frequency in radians per second thus ω = 2Πf
∞	Infinity. There is no such quantity but, it can be argued, there is such a number, OR is that the other way around - who cares? This quantity may not actually occur in real circuits but the impedance of a parallel LC circuit using perfect components is mathematically infinite.
\| \|	A symbol for an unknown value enclosed in two vertical lines means the absolute value of the quantity thus \|Z\| is the absolute value of impedance and has no direction, +ve or -ve.