Before discussing voltage dividers let's look at a different style of
drawing schematics. Schematics can get complicated and hard to follow.
To make things simpler designers often leave out the battery and the
connections to it.
The circuit to the left is the same as the circuit to the right. The
circle connects to the positive terminal of the 12 volt battery and the
ground symbol connects to the negative terminal.
Where a part of the circuit connects to
the battery a circle with a voltage next to it denotes the connection.
If there are multiple batteries the appropriate connections and
voltages are labeled. A ground symbol denotes the connection to the
appropriate ground point. The example above has only one battery so the
circle connects to the positive terminal and the ground symbol connects
to the negative terminal. This simplified style of schematic is used
below to explain voltage dividers.
As discussed above, when current passes through a resistor there is a
voltage differential across that resistor. The voltage is higher at the
side of the resistor where the current enters the resistor and lower at
the side where the current exits. You can take advantage of this
property to reduce voltage when needed. A circuit that does this is
called a voltage divider.
Voltage division is simply a manifestation of Kirchhoff's Voltage Law.
If you have two resistors in series, some of the total voltage will be
seen across one resistor and the rest of the voltage across the other.
If the two resistors are of equal value, the voltages across them will
be equal. For example, if you have 18 volts across two 100 ohm
resistors in series, each resistor will have 9 volts across it,
totaling the original 18 volts.
Two equal resistors in series will have equal voltage. Measured
compared to ground the voltage between two resistors will be ½ the
total voltage (the line next to the “+9V” is just to show where the
voltage is measured).
If one resistor is of a greater value than the other, it will have
proportionally more voltage across it. For example, if you have 18
volts across a 100 ohm and a 200 ohm resistor in series, the 100 ohm
resistor will have 6 volts across it and the 200 ohm resistor will have
12 volts across it, again totaling the original 18 volts.
If the resistors are not equal, the voltages change proportionally.
They still add up to the total voltage. The voltage between the
resistors, compared to ground, will be the voltage across the resistor
connected to ground. Here the 200 ohm resistor is connected to ground.
There are 12 volts across that resistor. Therefore, the voltage between
the resistors is +12 volts.
Notice that we have not concerned ourselves with how much current is
flowing. As far as voltage division is concerned it doesn't matter. If
you have 18 volts across two resistors in series, and one resistor has
twice the resistance as the other, the lower value resistor will have 6
volts across it and the higher value resistor will have 12 volts across
it, again totaling the original 18 volts.
It doesn't matter what the actual resistors are. As long as the
proportions don't change, the voltages don't change. These voltage
dividers have radically different resistors, but since the proportions
are the same the voltages are the same.
The only difference is that the circuit with 300 ohms total resistance
has a current of 60 mA (0.06 A) and the circuit with 3,000,000 ohms
total resistance has a current of 60 μA (0.00006 A).
A little trick
To find the voltages across the resistors in a voltage divider, divide
the total voltage by the sum of the ratio of resistance. The above
examples have a resistance ratio of 2:1. The sum of 2:1 is 3 (2 + 1 =
3). Divide the total voltage by this sum. That is 6 in this case (18
3 = 6). That is the voltage across the lesser resistor, 6 volts here.
The greater resistor will have twice this value, 12 volts in this case.