Part 1: Fundamental Concepts: Voltage Dividers

When two or more resistors are connected in series, the total voltage applied to them is divided and appears across each resistor. This is such a useful thing to have happen that two resistors connected in series has been given a unique name. This simple arrangement, shown in the following figure, is referred to as a voltage divider. Voltage dividers are used to provide a percentage of the voltage applied to them as an output.

Schematic diagram of a voltage divider showing current flow.

Figure 1. A voltage Divider.

To find the value of Vout, you can first calculate the current flowing in the circuit and then determine the voltage across R2. Given how common voltage dividers are, it is worthwhile to develop an equation that solves for the value in one step. Using Ohm’s Law, Vout is found by:

V = I * R ;Ohm's law

Rtotal = R1 + R2 ;Total resistance

Vin = I * (R1+R2) ;Put in (R1 + R2) for R

I = Vin/(R1+R2) ;[1] Rearrange to find I

Vout = I * R2 ;[2] Voltage across R2

Vout = (Vin/(R1+R2)) * R2 ;Put in I from [1] into [2]

A much easier to read version of the final equation above is shown in the following equation. This equation is worthwhile committing to memory.

Equation 1. Equation for voltage divider.

Voltage dividers cannot drive any load without changing the Vout value. For instance, if you connect a resistor, or something else that causes current to flow from the top of R2, Vout will decrease. There are other circuit elements, discussed later, that can be used to overcome this limitation.