Lesson 3: Series and Parallel Circuits.



When two or more components are connected in a circuit they are said to be in one of 2 configurations, either in Series or in Parallel. Each configuration gives a different total, and each total can be worked out by a different formula. Resistors in Series.

The first and simplest configuration we will look at is Series. The diagram on the right shows 2 resistors connected in series, and the formula to calculate the total resistance is simply Rtotal = R1 + R2. In this case its Rtotal = 10 ohms + 10 ohms which is of course a total of 20 ohms. Lets look for a moment at what happens to the other elements in the circuit. The same current flows through both resistors so, using Ohm's law, the total current will be the total voltage divided by the total resistance.(E=IR so I=E/R) I = 12volts divided by 20 ohms which equals 0.6 amps.

The voltage distribution takes a little more thought. In fact it is directly proportional to the valuse of the resistors. In the example both resistors are the same so the voltage across each resistor will be exactly the same. The voltage at the middle point would read 6 volts. However, if one of the resistors was 20 ohms and the other 10 ohms, then 2/3 of the voltage (8 volts) would be across the 20 ohm resistor and 1/3 (4 volts)across the 10 ohm, and if one was 30 ohms and the other 10 ohms, then 3/4 of the voltage would appear across the 30 ohm and 1/4 across the 10 ohm, and so on...

Christmas tree lights are usually connected in series, and thats why if one bulb blows the whole string stops working.

Resistors in Series.
Parallel circuits have a simple voltage distribution. Every component gets the same voltage. This is the system your household electricity works on. On the other hand every component has its own current flow dependant on the value of the resistor, and the total current is the sum of the individual currents. For example: R1 has a value of 10 ohms so the current flowing through it is (I=E/R) 12 volts divided by 10 ohms which is 1.2 amps. R2 has a value of 20 ohms so the current flowing through it is 12 volts divided by 20 ohms which is 0.6 amps, so summing them the total current flowing through the amp meter is 1.2 amps + 0.6 amps which equals 1.8 amps. Not difficult...

The total resistance is a different story. The formula for parallel resistors is
   1    =  1   +   , now lets put some values in it.
RTotal     R1       R2

   1    =  1   +   =   2   +   =   3  but this is not the final answer.
RTotal     10       20     20       20     20

To find out what RTotal is we must first put the above result in the format
   1    , therefore we must divide the top by 3 to get the 1, and we must
RTotal

divide the bottom by 3 also to keep the fraction in proportion, so the real value of RTotal is 20 divided by 3, which is 6.6666...ohms. The battery can not tell the difference between a 6.67ohm resistor and a combination of a 10 ohm and a 20 ohm resistor connected in parallel.

The exact same principle applies to speakers connected in parallel to an amplifier. Two 8 ohm speakers connected in parallel look like one 4 ohm speaker to the amplifier, and three 8 ohm speakers in parallel looks like one 2.67 ohm speaker to the amplifier, etc.




We're now ready to move on to the next lesson. Click here to go to the lesson about frequency reactive components, or click here to return to the Electronics for Sound Techs index page.