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The Foundation Course doesn't involve much mathematics, just Ohms Law and the Power Calculation.

Ohms Law

Ohms law shows the relationship between Voltage (V), Current (I) and Resistance (R)

A 9 Volt battery has an output of approximately 9V (depending on the state of charge) and if you connect a circuit between the Positive (+) terminal and the Minus (-), a Current will flow from +ve through the circuit to the -ve, the quantity of current is determined by the resistance (measured in Ohms) of the circuit and is measured in Amps (A).

Ohms law is normally shown as: V = IR or Voltage is equal to the Current multiplied by the Resistance.

This can also be expressed as I = V/R or as R = V/I

In a practical sense you may wish to work out the resistor you need to use with an LED supplied from a 9V battery

A red LED is likely to drop 1.8Volts (although it is always best to check the data sheet), so you subtract 1.8V from 9V giving 7.2V

When dealing with small currents, voltages or resistances we sometimes use a prefix to indicate a 1000th (milli) or 1,000,000th (micro)

These are usually shortend to m for milli and μ for micro (note: use a μ symbol not a u symbol)

When dealing with large currents, voltages or resistances we sometimes use a prefix to indicate thousands (Kilo) or Millions (Mega)

These are usually shortened to K for Kilo and M for Mega

If you want the LED to be really brightly lit you may want to use a current of 20mA (0.02A), but for a low power circuit you may want to use a current 1mA (0.001A).

So to calculate the Resistor you can use R = V/I or R = 7.2V / 0.001A, which gives 7200 ohms.

The nearest larger preferred value (the nearest larger value that is easily available) is 7500 ohms or 7.5K ohms

This could also be written as 7.5K Ω or 7K5 Ω

Resistor are sold in standard ranges of values, these values are called preferred values.

The values are split into decades, and the name of the ranges are prefixed by an E, the E12 range has 12 values per decade and for the 10 to 100 decade the E12 range would be made up of the following values:

10 Ω, 12 Ω, 15 Ω, 18 Ω, 22 Ω, 27 Ω, 33 Ω, 39 Ω, 47 Ω, 56 Ω, 68 Ω, 82 Ω

The range of resistors commonly available are from around 1 Ω to 10 MΩ although larger and smaller resisters can be obtained.

When designing electronic circuits one would usually use the E24 range of values (24 values per decade), the 100 to 1000 decade would be as follows:

100 Ω, 110 Ω, 120 Ω, 130 Ω, 150 Ω, 160 Ω, 180 Ω, 200 Ω, 220 Ω, 240 Ω, 270 Ω, 300 Ω, 330 Ω, 360 Ω, 390 Ω, 430 Ω, 470 Ω, 510 Ω, 560 Ω, 620 Ω, 680 Ω, 750 Ω, 820 Ω, 910 Ω,

Resistors are also available in E48, E96 and E192 ranges, but most designs don't require such exact values.

You don't need to memorise these values, but having a rough idea of what is available is useful background knowledge.

Power Calculation

Power (P) is measured in Watts (W) and is a measure of energy, it is the result of Current (I) flowing through a circuit and the Voltage (V) across it.

Power is calculated multiplying the Voltage accross a circuit by the Current flowing through it and can be expressed as follows

The standard formula is P = V * I

This can also be expressed as V = P/I or I = P/V a practical example is as follows

To work out how much power a 50 ohm resistor with 100 Volts across it is going to have to dissipate, you need to use P = V * I to get the Power, however as you don't have the currrent (I) you will need to use ohms law to get that first.

Using I = V/R gives I = 100/50 = 2 Amps

Then using P = V * I gives P = 100 * 2 = 200Watts