Why Your Voltage Divider Output Changes When You Connect a Load

Alternative titles

1. Voltage Dividers Are Not Voltage Regulators: Understanding the Loading Effect
2. The Missing Resistor in Your Voltage Divider Calculation
3. Why a 3.33 V Divider Can Become a 2.5 V Node

Short description / excerpt

A voltage divider can produce the expected voltage in a textbook calculation and still shift when another circuit connects to its output. This worked example shows why the load becomes part of the divider, how to calculate the new output, and when a divider is appropriate in a real design.

Article

A voltage divider gives 3.33 V on paper.

You connect something to the output.

Now the voltage is closer to 2.5 V.

Why?

The formula was not wrong. The circuit changed.

This is the voltage-divider loading effect: the thing connected to the output is not invisible. If it draws current, it changes the effective resistance seen by the divider and therefore changes the output voltage.

The ideal voltage divider

The familiar two-resistor divider has an input voltage, a top resistor R1, and a bottom resistor R2 connected to ground. The output is measured at the node between the two resistors:

Vin ── R1 ──┬── Vout
            │
            R2
            │
           GND

With no external load, the output is:

Vout = Vin × R2 / (R1 + R2)

This equation assumes that the output measurement draws negligible current. That assumption is often useful, but it is still an assumption.

A worked 5 V example

Take the following values:

• Vin = 5 V
• R1 = 10 kΩ
• R2 = 20 kΩ

The unloaded output is:

Vout = 5 × 20 / (10 + 20)
     = 100 / 30
     = 3.333 V approximately

The current through the series divider is:

I = 5 / (10 kΩ + 20 kΩ)
  = 166.7 µA approximately

So far, the result is exactly what we expect.

What changes when a load is connected?

Now connect a load resistor of 20 kΩ from Vout to ground:

Vin ── R1 ──┬── Vout
            ├── R2 ── GND
            └── RL ── GND

The important detail is the connection location. Both R2 and RL connect between the same two nodes: Vout and ground. That means they are in parallel, not in series.

The load therefore becomes part of the voltage-divider calculation.

Replace the lower branch with an equivalent resistance

The parallel equivalent of R2 and RL is:

Req = R2 || RL
    = (R2 × RL) / (R2 + RL)

For two 20 kΩ resistors:

Req = 20 kΩ || 20 kΩ
    = 10 kΩ

The loaded circuit is now equivalent to a 10 kΩ top resistor in series with a 10 kΩ lower branch. Reapplying the divider equation:

Vout_loaded = 5 × 10 / (10 + 10)
            = 2.5 V

The output did not move because the original formula stopped working. It moved because the lower resistance changed from 20 kΩ to 10 kΩ.

The current through R1 is now 250 µA. At the output node, that current splits between R2 and RL. Since both branches are 20 kΩ and both have 2.5 V across them, each branch carries 125 µA.

Quantifying the loading error

Comparing the ideal and loaded results:

loading error = (3.333 - 2.5) / 3.333 × 100%
              ≈ 25%

A 25% shift is large enough to break many designs that looked correct when only the unloaded formula was considered.

Why this matters in real circuits

The load does not have to be an obvious resistor. It can be the input network of another circuit, a measurement instrument, a sensor interface, a bias network, or an ADC input. In each case, the next stage has some finite input impedance and may also have leakage or bias currents. From the divider's point of view, that next stage is part of the load.

For a high-impedance measurement input, the loading may be small compared with R2. For a lower-impedance input, it may be significant. The right question is not simply “What voltage does the divider formula give?” It is “What impedance does the next stage present to this node?”

A common mistake

The most common mistake is to calculate Vout from R1 and R2, then connect a load without recalculating. A related mistake is to treat the load as if it were in series with R2 because it appears later in the signal path. Topology matters more than drawing order: components sharing the same two nodes are parallel.

A useful design intuition

There is another way to see the same result. Before a load is attached, the divider can be viewed from its output node as a Thevenin source. Its open-circuit voltage is the ideal 3.333 V, and its source resistance is:

Rth = R1 || R2
    = 10 kΩ || 20 kΩ
    = 6.667 kΩ approximately

When a load is connected to that source, the load and Rth form another divider. A 20 kΩ load is not enormously larger than 6.667 kΩ, so it causes a noticeable drop. This viewpoint is useful when evaluating a divider as the source for a later stage: a low source resistance makes the node less sensitive to loading, but lowering both divider resistors also increases the continuous current drawn from Vin.

That tradeoff is why simply making every resistor smaller is not a complete design rule. Smaller values can reduce the percentage error from a given input impedance, but they consume more power and may be inappropriate for a battery-powered circuit. A buffer can provide a high input impedance and a low output impedance when the application needs both low loading and useful drive capability.

The same reasoning applies to a multimeter or oscilloscope probe. The instrument has a specified input resistance, so it can be modeled as another load. If that resistance is many times larger than R2, the measurement error may be small. If it is comparable to R2, the measurement is part of the circuit and must be included.

When is a voltage divider appropriate?

A divider is useful when the output is a signal or reference that will feed a high-impedance input and only a small current is required. It is also useful for sensing, setting bias levels, and creating a simple threshold reference when the tolerance and source impedance are acceptable.

It is not a good general-purpose replacement for a regulated supply. A divider's output changes with its input, resistor tolerance, temperature, and load current. If a downstream circuit needs a stable voltage or meaningful power, consider a buffer, voltage regulator, or another circuit designed for that job.

If you want to experiment with different resistor and load values, the CircuitClarity Voltage Divider Calculator shows both the ideal divider and the loaded result so the effect is visible as the circuit changes.

The useful habit is simple: whenever something connects to a divider output, add that connection to the circuit model before trusting the number.

Recommended DEV tags

electronics embedded engineering beginners