Part 1: Fundamental Concepts: Series Circuits

This section continues the investigation of what happens when we follow the pattern of having resistors connected end to end.  When components are connected in this way (end to end), it is called a series connection.  This is because the current must flow though each component in turn, or in series, to return to its source.  A series circuit with three resistors, all of equal value, and a voltage source is shown in the following figure.  Series circuits aren’t required to have all of the values the same.  In this example, they are simply for convenience.

As a side note, typically when drawing a schematic, the first component of a particular type is given its reference designator, which is R for resistors, followed by the number 1. The second is followed by a 2, and so on.  Therefore, if there were three resistors in a circuit, they would be labeled R1, R2, and R3.  This is not mandatory, but it is the way that schematics are most frequently drawn. Figure 1. Three series resistors and a voltmeter.

You can find the voltage across any of the resistors shown in Figure 1, usually called the voltage drop, if you know the current that is flowing through them and their resistance.  The same current, I, is flowing through each resistor in turn.  The magnitude of that current can be found by the voltage driving it and the total resistance of the circuit.  In a series circuit, the total resistance is the sum of the individual resistance values.  This makes sense given that the current must flow through each resistor in sequence, and each resistor contributes to the total resistance seen by the current as it flows.  This is analogous to the resistive rod example in the previous section.  The total resistance is equal to the sum of its parts.  The current, I, can therefore be found by Ohm's law using the sum of the resistance as follows:

V = I * R                           ;Ohm's law

6 = I * R                           ;Put in value for V

6 = I * (100+100+100)     ;Put in the value for R

I = 6 / (100+100+100)     ;Rearrange

I = 0.02A                          ;Solve for I

With the value of the current in hand (0.02A), we can find the voltage drop across any of the resistors in the circuit.  In this case, they are equal in value so finding the voltage drop across any resistor will tell us what we need to know.

V = I * R                            ;Ohm's law

V = 0.02 * 100                   ;Put in I and R

V = 2V                               ;The voltage drop

This tells you that the voltage drop across each resistor is 2V.  This make a lot of sense.  Look at the following figure, which is the same as Figure 1, with each voltage drop indicated, as well as the total drop across all three resistors. Figure 2. The voltage drop across each resistor.

Each of the three resistors has a voltage drop of 2V appearing across it, as expected, for 0.02A flowing through a 100Ω resistor.  The voltage drop across all three resistors is therefore 6V.  This has to be the case because the voltage source in this circuit is 6V, and its connection to the resistors is though conductors which are lossless.  The sum of the voltage drops across the series connected resistors must be equal to the voltage applied across all three of them.

Voltages sources have a polarity.  A voltage source’s current flows from the positive terminal and returns to the negative terminal.  The voltage drops that appear across the resistors also have a polarity.  This is because, in a resistor, electrical energy is converted to heat when current flows through it.  As a consequence, there is a loss of potential in the direction of the current flow.  This means that the resistor’s terminal the current flows into, must be more positive than the terminal it leaves.  Figure 3 is shown below with polarity indications on the resistors to indicate the polarities of the voltage drops. Figure 3. The polarity of the voltage drop across each resistor.

Looking at Figure 3, it may seem odd to you that the junction between R1 and R2 have a “+” and “-“ adjacent to each other.  This occurs again at the junction between R2 and R3.  How can that be?  The answer is simple if you remember that all voltages are measured between two points in a circuit.  In other words, all voltage measurements are made in reference to, or relative to, another point in the circuit.  Both the voltage drop across each resistor, and the polarities of those voltage drops, are unique to that resistor.  It all depends on the two points across which we choose to measure the potential difference.  If you were to choose different points to measure the voltages from and to, you would get a different result.  This is shown in the following figure. Figure 4. The voltage drops from a common point.

In Figure 4, all of the voltages are shown in reference to a common point.  That point happens to be the point in the circuit with the lowest potential.  As a consequence, all of the values shown (+2V, +4V, and +6V) are positive.  The important point to remember here is that all voltages are really a measure of potential difference.  Therefore, every voltage is a measurement relative to some other point in the circuit. Current is different.  It is a measurement of the number of charges that are moving in the circuit.  Therefore, a current is indicated with a direction of flow.  Current flows from a more positive to less positive potential.

Key Concepts

• All voltage measurements are made relative to another point in the circuit.

• Current is charge flow through a portion of a circuit and is not measured in relationship to another point.

• When a number of resistors are connected in a chain, it is called a series connection.

• Ohm’s Law applies universally.  In a series connected circuit the voltage across each resistor can be found from the current flowing through it and its resistance.

• The voltage across individual series connected resistors add up to the voltage across the entire chain.