Resistors in Series
We say that two resistors are in series when there is one terminal of one resistor connected to one terminal of the other resistor, and nothing else is connected to this connection point.
As it is shown, there are no extra branches between R1 and R2. The current that gets out of R2 goes directly into R1 (there is no other place to go), therefore the same current flows through both resistors.
If we connect two resistors in series, the equivalent resistance is the sum of both resistors values:
Obviously the total resistance will be bigger than any of the individual resistors which means that we are offering more resistance to the current flow. The current intensity can be calculated with the Ohm Law:
For example, look the next circuit, where there are two resistors in series R1 and R2, connected to a 12V voltage source.
The total equivalent resistance is:
And the current in amperes:
Knowing the current, we are able to calculate the voltage drop over each resistor (V1 and V2), applying the ohm law individually:
Thus, on one resistor there is a voltage drop of 8 volts, and 4 volts on the other one, totalizing 12 volts which is the applied source voltage.
Note that resistors in series act as a voltage divider because the voltage in the intermediate point between resistors is a fraction of the total voltage applied to the pair. For instance, if the resistors are equal (regardless their values), the voltage in the intermediate point will be half the source voltage. No need to calculate the current to know that. Here we have the general expressions for the output voltages V1 and V2, valid for any value of Vdc, R1 and R2.
This effect is widely used, particularly in potentiometers and presets.
You're probably familiar with the appearance of these devices, they are usually used to adjust the volume of audio equipments and the signal level in different applications.
But, what is there inside?
Into the potentiometer we have a resistor, there are two external terminals that are connected to the resistor ends, and the third terminal is connected to an intermediate point, splitting the resistor in two parts, we can name this parts as R1 and R2. The arrow indicates that this intermediate point is movable, so what we have is basically two resistors in series where the value of the resistors R1 and R2 are variable, while the end-to- end resistance value (R1+R2) is constant.
Applying the voltage divider general expression to this circuit, we get the output voltage as a function of the input voltage:
Thus, this circuit converts an input voltage Vin in a lower voltage Vout, and the output value can be adjusted with a knob or with a screw. Preset type uses a twenty-turns screw, which is specially suited for precision applications.
It is important to remember that all this works because the resistors are in series, then no significant current derives from the mid point between resistors to another branch of the circuit. If you tried to use Vout to feed another component as a LED for example, the equation would not be valid, and Vout would change its value.
Resistors in Parallel
We say that two resistors are in parallel when they have both terminals connected to each other´s.
Both resistors are under the same tension, and total current is derived in two branches. The current on each branch depends only on Vdc and the resistor on this branch, and it is independent on what happens in the other branch. The total current exiting the battery positive pole is the sum of I1 and I2, and it is the same that returns to the negative pole (as always). The parallel can be considered as only one equivalent resistor, which value is obtained with the last equation below.
When we put two (or more) resistors in parallel, we are giving a wider and easier path to the current flow, which means less resistance. That's why the equivalent total resistance will result lower than the value of any of the resistors taken individually.
Let's see this example, with resistors of 6 and 3 ohms:
We can calculate the total equivalent resistance, and the current in each branch. Then we can verify that the total current calculated by ohm law with the total resistance is equal to the sum of currents on each branch.
This is enough about resistors by now. On the next chapter we will introduce alternate current circuits and power transformers.