# Regarding the design of a basic voltage divider

I've just entered the fabulous world of circuitry and was wondering about the design of voltage dividers. I understand their function and formula quit well, but was wondering about the actual structure of the voltage divider.

In the picture below, there are two resistors and Vout is between R1 and R2. I was wondering why Vout is placed exactly there as opposed to after R2 and if the placement would actually make any difference in Vout?

In general, voltage division applies to the voltage across a resistor in series with one or more other resistors.

For example, assume that we have $N$ series connected resistors and, further, that the voltage across the series combination is $V_S$.

Then, the voltage across the $n^{th}$ resistor is given by the general voltage division formula:

$$V_{R_n} = V_S \frac{R_n}{R_1 + R_2 +\; ... \; + R_{N-1} + R_N} =$$

In the diagram you provide, it happens to be the case that

$$V_{out} = V_{R_2}$$

And, by the general voltage division formula applied to two series connected resistors

$$V_{R_2} = V_{in} \frac{R_2}{R_1 + R_2}$$

Thus,

$$V_{out} = V_{in} \frac{R_2}{R_1 + R_2}$$

Note that we could have chosen $V_{out}$ to be the voltage across $R_1$ instead though this isn't often the case.

In most cases, the output voltage is referenced to ground and, so, the output voltage is taken across the resistor with one terminal grounded.

In summary, voltage division is more general than the two resistor voltage divider circuit you've provided. The principle of voltage division and the general formula is a valuable 'tool' in one's circuit solving 'toolkit'.

If it is placed after R2 then it will have the same potential as ground, 0 volts. We put it before R2 so that its potential is the same as the drop across R2.

• Thanks for clarifying. I'm now wondering - would there be any case in which more than 2 resistors are used and in such a case what would the placement of the different Vouts be? – The Ideasmith Nov 12 '14 at 0:41
• If you had three resistors in series in a voltage divider, you could get two different output voltages at the two junctions between resistors. Note that any load you place on the "output" of a voltage divider is effectively another resistor in parallel with the resistors below that output, so will affect the output voltage. – Peter Bennett Nov 12 '14 at 0:46