Tristan s Guide to: Solving Series Circuits. Version: 1.0 Written in Written By: Tristan Miller Tristan@CatherineNorth.com

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1 Tristan s Guide to: Solving Series Circuits. Version: 1.0 Written in 2006 Written By: Tristan Miller Tristan@CatherineNorth.com

2 Series Circuits. A Series circuit, in my opinion, is the simplest circuit to solve. The definition of Series is: Similar things placed in order or happening one after another. This means, things that happen one after another. Let s look at a sample Series circuit. Here, we have 4 Resistors. R1, R2, R3 and R4. The Resistors are connected in Series with the battery, E1. When the electrons leave the Positive side of the battery, they travel down the wire, and into Point A on R1. The electrons travel through R1, then down the short wire to the right of R1, and into the left side of R2. Through R2, then through R3, then through R4, and the electrons finally return to the Negative side of the battery. The red arrows show how the electricity will travel in this circuit. (Conventional Theory) From the battery, Through R1, and then through R2, and then through R3, and then through R4, and then back to the battery. Tristan Miller s Guide To Solving Series Circuits Ver:

3 Calculating Total Resistance in Series Circuits. The circuits Total Resistance is very easy to calculate. Because the resistors are in a straight line, the Total Resistance is equal too all the resistor values added together. Let s throw some random numbers into the circuit from the last page. These are just made up numbers, they can be any value; it does change how we solve it. R1 is 500 Ohms R2 is 600 Ohms R3 is 40 Ohms R4 is 790 Ohms E1 is 10 Volts. As I said before, the Total Resistance is equal to all of the Resistor s values added together. In an equation, Total resistance can be written as RT. RT = R1 + R2 + R3 + R4 That is the equation for this circuit. All of the resistor s values added together, equal the Total Resistance. To use this equation, you just have to substitute the numbers that you know, into the right spot. RT = R1 + R2 + R3 + R4 RT = 500 Ohms Ohms + 40 Ohms Ohms RT = 1930 Ohms. Therefore, the total resistance of the circuit is 1930 Ohms. Let s say you had a Series circuit with 6 resistors in it. You use the same process to find the total resistance. Add all the resistor values together. RT = R1 + R2 + R3 + R4 + R5 + R6 It will be the same if you have 2 resistors, or 1000 resistors. Add each and every resistor together, to find out the total resistance. Tristan Miller s Guide To Solving Series Circuits Ver:

4 Calculating an Unknown Resistor Value Let s say you re given a circuit, with 3 resistors in Series. You re told the Total Resistance, and Two of the resistor s values. You can rearrange the formula to find out what the Unknown Resistor s value is. Let s use this random circuit as an example. The Total Resistance, RT, is 200 Ohms. R1 is 30 Ohms R2 is 100 Ohms R3 is Unknown. The formula for the Total Resistance is; RT = R1 + R2 + R3 Let s put the values we know, into that formula. 200 Ohms = 30 Ohms Ohms + R3 What we want to do now, is get R3 by its self, on one side of the = sign. Subtracting R1 and R2 from each side of the = sign will give us R3 by its self, on the right of the = sign. RT R1 R2 = R1 R1 + R2 R2 + R3 This formula can now be simplified, because R1 R1 = 0 and R2 R2 = 0 RT R1 R2 = R3 Let s substitute the numbers in again, and solve it. 200 Ohms 30 Ohms 100 Ohms = R3 170 Ohms 100 Ohms = R3 70 Ohms = R3 Therefore; R3 is equal to 70 Ohms. Tristan Miller s Guide To Solving Series Circuits Ver:

5 Calculating The Current in a Series Circuit. The current that flows through a Series Circuit is the same at any point in the circuit. Let s use the first circuit as our example. The current that is flowing through R1, is the same as the current that is flowing through R2, and R3, and R4. This is because all of the electrons have to go through each resistor, before they return to the battery. To find out the Current that is flowing through the entire circuit, we use the formula: Voltage E Total Current = Or: IT = Total Resistance RT Remember this circuit? We already calculated the Total Resistance of the circuit; it was 1930 Ohms. E1 is 10 Volts. Tristan Miller s Guide To Solving Series Circuits Ver:

6 Let s enter these two values into the formula. E 10 Volts IT = = = Amperes RT 1930 Ohms This is a ridiculously long number, and should be rounded in most cases. Let s round it to 8 decimal places Amperes This still looks weird, so let s convert it into Milliamps. 1 Amp is equal to 1000 Milliamps. Multiply the calculated ampere value by 1000, and we will have the value in Milliamps Amps * 1000 = Milliamps Therefore, the current that is flowing through our circuit, is mA. This also means that there is mA flowing through each resistor in our circuit. As you can see, I ve placed 5 Amp Meters into the circuit. All of the meters show the same reading of 5.18 ma. This is the same number that we calculated. This just shows you that the current is the same at any point in the circuit. So; IT = I1 = I2 = I3 = I4 Tristan Miller s Guide To Solving Series Circuits Ver:

7 Calculating Total Current Using Voltage and Current. Let s say you are given a circuit, and you want to know what the Total Resistance of the circuit is. IT is 50 Milliamps. E1 is 10 Volts. We use the following formula to calculate the Total Resistance. Voltage E Total Resistance = or: Total Current IT We have to convert the number 50mA into Amperes. To do this, we divide our Milliamp value by So: 50mA = A 1000 Let s enter our numbers into the formula. E 10 Volts = = 200 Ohms. IT Amps So the total resistance in this circuit is 200 Ohms. Tristan Miller s Guide To Solving Series Circuits Ver:

8 Calculating Voltage with Total Current and Total Resistance. IT is 150mA. R1 is 60 Ohms. E1 is Unknown. We use this formula to calculate the Voltage. Voltage = Current * Resistance or: E = I * R or simply written as: E = IR First we convert the 150 ma value into Amperes, by dividing the ma value by mA = A 1000 Let s enter our values into the formula. E = I*R E = 0.150Amps * 60 Ohms E = 9 Volts Tristan Miller s Guide To Solving Series Circuits Ver:

9 Calculating the Voltage across a Resistor with the Current. Going back to the first circuit, let s find the voltage that is across each resistor. R1 is 500 Ohms. R2 is 600 Ohms. R3 is 40 Ohms. R4 is 790 Ohms. IT is 5.18mA. E1 is 10 Volts. Let s calculate the voltage across R1. We know that the current going through R1 is equal to IT. And we know that R1 has a resistance of 500 Ohms. Voltage across R1 = Current * Resistance of R1. ER1 = IT * R1. ER1 = A * 500 Ohms. ER1 = 2.59 Volts. So, the voltage across R1 is 2.59 Volts. To calculate the voltage across the other resistors, we use the same formula, except R1 is replaced by the number of the resistor that you are calculating the voltage of. Tristan Miller s Guide To Solving Series Circuits Ver:

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