Browser note: Your Web browser should be capable of displaying symbols. Here is the Greek letter omega: Ω. This looks like a W, instead of an omega, on some primitive browsers.

Printer note: Even if the document looks ok on your browser, it may still print bogus characters on your printer. If this happens, see if you can get an update on your printer driver.

Note that current is defined as the flow of **positive** charges.

Resistance, frequency, power, etc. values are frequently expressed using
prefixes which stand for powers of ten. For example, a 12 MΩ resistor has
a resistance of 12×10^{6} Ω. You should know the designations of
powers of ten in the table below.

Prefix |
Name |
Value |

f | femto | 10^{-15} |

p | pico | 10^{-12} |

n | nano | 10^{-9} |

µ | micro | 10^{-6} |

m | milli | 10^{-3} |

k | kilo | 10^{3} |

M | mega | 10^{6} |

G | giga | 10^{9} |

T | tera | 10^{12} |

P | peta | 10^{15} |

E | exa | 10^{18} |

Commit them to memory.

Many resistors have colored stripes to indicate the resistance value and the
tolerance. Here you will find out how to use the resistor color code: http://micro.magnet.fsu.edu/electromag/java/resistor/.
When you need to, you can use the color code to determine the nominal value of
the resistor in ohms. Resistor values are not exact; the *tolerance* of
the resistor indicates the accuracy of the resistor value. For example a 100
Ω resistor with a tolerance of 20% could have any value from 80 Ω
to 120 Ω. Low tolerance resistors are available for applications
requiring high precision.

Two elements are in series if they are connected together at one end with no other connection at that end. Use this definition, rather than your intuition, to determine if elements are in series. The following elements are in series:

These elements are not in series:

For resistors in series, the net resistance is just the sum of the individual resistances.

R_{EQ }= R_{1} + R_{2} + ..... R_{n}

Two elements are in parallel if both ends of each element are connected together. These elements are in parallel:

These elements are not in parallel:

A parallel combination of resistors is found by the equation

1/R_{EQ} = 1/R_{1} + 1/R_{2} + 1/R_{3} +
..... 1/R_{n}

A useful special case is for exactly two resistors in parallel:

R_{EQ} = R_{1}R_{2}/(R_{1} + R_{2})

The equations for elements in series and parallel are easily derivable from Kirchhoff's Laws.

Before going on, you should complete Tutorial 2 **on resistors
in series and parallel**.

Some circuits, such as the one shown below, cannot be simplified by combining elements in series and parallel. When this happens, you just have to grit your teeth and apply Kirchhoff's Laws, or use the delta-wye transformation (discussed in a later section).

Another useful concept in analyzing circuits is that when no current flows through a resistor, capacitor, or inductor, that element can be ignored (removed) when making calculations. A resistor that is connected to the same point on each end is shorted. A resistor with a floating end (not connected to anything) is open circuited.

The voltage divider equation will be very useful to you. Consider the figure below.

It is easily derivable from Kirchhoff's Laws that

V_{2} = V_{S}R_{2}/(R_{1} + R_{2})

Knowing when (and when not) to use the voltage divider equation can save you
time and protect you from error. This equation cannot be used if something is
connected to V_{2} that draws current.

The current divider equation may be occasionally useful. Consider the figure below.

Similar to the voltage divider equation, Kirchhoff's Laws can be used to find that

I_{2} = I_{S}R_{1}/(R_{1} + R_{2})

Notice that the numerator term uses the resistor that the current
**doesn't** go through.

At this time you should complete Tutorial 2A on **voltage
and current dividers**.