This post explains some basic calculations with resistors and voltage dividers.
Resistors in series
When resistors are used in series, we can simplify the circuit to make calculations easier.
As shown in figure 1, if we have two resistors in series with values Ra and Rb, the equivalent resistance is the sum of both.
Figure 1 – Simplification of a circuit with 2 resistors in series.
Using Ohm’s law, this makes it much easier to calculate the current flowing in the circuit:
In figure 2, a more generic example is shown, where there are n resistors in series.
Figure 2 – Generic case where n resistors are in series.
In this case, the equivalent resistor has a value equal to the sum of the values of each resistor in series, as shown below:
Resistors in parallel
When resistors are used in parallel, as shown in figure 3, it’s also possible to simplify the circuit.
Figure 3 – Simplification of a circuit with 2 resistors in parallel.
In this case, the equivalent resistance is given by the equation below:
Once we have the equivalent circuit, we can calculate the current flowing with the same equation used before.
Figure 4 – Generic case where n resistors are in parallel.
Then again, in the generic case with n resistors in parallel, we have the equation bellow:
The voltage divider is a very simple circuit that can be used to lower a certain voltage. The circuit, shown in figure 5, is the same as the one shown in figure 1.
Figure 5 – Voltage divider circuit.
As stated before, we know that current is given by:
Using Ohm’s Law, we know that the voltage drop in Rb, which corresponds to Uout, is given by:
From this equation, is easy to conclude that if we use resistors with the same value we get an output voltage that is half of the input voltage.
Important: never use this method to create a power supply to your circuit. Besides being extremely inefficient, it will correspond to a load in parallel with Rb, which will affect the voltage levels. Check here for some suggestions for cheap power supplies.