The voltage divider or voltage divider consists of an association of resistors or impedances in series connected to a source. In this way, the voltage V supplied by the source -input voltage- is distributed proportionally in each element, according to Ohm’s law:
V i = IZ i .
Where V i is the voltage across the circuit element, I is the current flowing through it and Z i the corresponding impedance.
When arranging the source and the elements in a closed circuit, Kirchhoff’s second law must be fulfilled, which states that the sum of all the voltage drops and rises is equal to 0.
For example, if the circuit to be considered is purely resistive and a 12 volt source is available, simply by placing two identical resistors in series with said source, the voltage will be divided: each resistance will have 6 Volts. And with three identical resistors you get 4 V in each one.
Since the source represents a voltage rise, then V = +12 V. And in each resistor there are voltage drops that are represented by negative signs: – 6 V and – 6 V respectively. It is easy to see that Kirchoff’s second law is fulfilled:
+12 V – 6 V – 6 V = 0 V
This is where the name voltage divider comes from, because through series resistors, lower voltages can easily be obtained starting from a source with a higher voltage.
The voltage divider equation
Let’s continue considering a purely resistive circuit. We know that the current I through a circuit of series resistors connected to a source as shown in figure 1 is the same. And according to Ohm’s law and Kirchoff’s second law:
V = IR 1 + IR 2 + IR 3 +… IR i
Where R 1 , R 2 … R i represents each series resistance of the circuit. Thus:
V = I ∑ R i
So the current turns out to be:
I = V / ∑ R i
Now let’s calculate the voltage across one of the resistors, the resistor R i for example:
V i = (V / ∑ R i ) R i
The previous equation is rewritten as follows and we have the voltage divider rule ready for a battery and N resistors in series:
Voltage divider with 2 resistors
If we have a voltage divider circuit with 2 resistors, the above equation becomes:
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