Voltage divider circuits

Voltage divider circuits

Let's analyze a simple series circuit, determining the voltage drops across individual resistors:

From the given values of individual resistances, we can determine a total circuit resistance, knowing that resistances add in series:

From here, we can use Ohm's Law (I=E/R) to determine the total current, which we know will be the same as each resistor current, currents being equal in all parts of a series circuit:

Now, knowing that the circuit current is 2 mA, we can use Ohm's Law (E=IR) to calculate voltage across each resistor:

It should be apparent that the voltage drop across each resistor is proportional to its resistance, given that the current is the same through all resistors. Notice how the voltage across R₂ is double that of the voltage across R₁, just as the resistance of R₂ is double that of R₁.

If we were to change the total voltage, we would find this proportionality of voltage drops remains constant:

The voltage across R₂ is still exactly twice that of R₁'s drop, despite the fact that the source voltage has changed. The proportionality of voltage drops (ratio of one to another) is strictly a function of resistance values.

With a little more observation, it becomes apparent that the voltage drop across each resistor is also a fixed proportion of the supply voltage. The voltage across R₁, for example, was 10 volts when the battery supply was 45 volts. When the battery voltage was increased to 180 volts (4 times as much), the voltage drop across R₁ also increased by a factor of 4 (from 10 to 40 volts). The ratio between R₁'s voltage drop and total voltage, however, did not change:

Likewise, none of the other voltage drop ratios changed with the increased supply voltage either:

For this reason a series circuit is often called a voltage divider for its ability to proportion -- or divide -- the total voltage into fractional portions of constant ratio. With a little bit of algebra, we can derive a formula for determining series resistor voltage drop given nothing more than total voltage, individual resistance, and total resistance:

The ratio of individual resistance to total resistance is the same as the ratio of individual voltage drop to total supply voltage in a voltage divider circuit. This is known as the voltage divider formula, and it is a short-cut method for determining voltage drop in a series circuit without going through the current calculation(s) of Ohm's Law.

Using this formula, we can re-analyze the example circuit's voltage drops in fewer steps: