Interactive Animation: Functional Principle of a Voltage Divider

The following animation illustrates the functional principle of a voltage divider. Voltage dividers are of central importance for electrical signal processing.

Description

A voltage divider is a series circuit that divides an input voltage into two smaller output voltages. The magnitude of the output voltages depends on the ratio of the resistance values. The greater voltage drop occurs across the resistor with the higher resistance value. Voltage dividers reduce the voltage to a level suitable for subsequent circuits.

The animation illustrates this relationship through the blue voltage arrows next to the circuit: The arrows for V_RA and V_RPot share the total length of the V_total arrow between them. When you change the resistance value of the variable component using the slider on the left, the arrows adjust their length immediately. The larger voltage share always falls across the higher resistance.

Basics

The ratio of the output voltage to the input voltage is determined by the ratio of the resistance values.

\[ V_{out} = V_{in} \cdot \frac{R_2}{R_1 + R_2} \]

V_out: output voltage
V_in: input voltage
R₁, R₂: resistances of the voltage divider

You can verify this relationship directly in the animation: Use the input field to set the value of R_A between 100 and 9,000 Ω. Adjust the second resistance using the slider on the left. The resulting voltage values V_RA and V_RPot are displayed numerically next to the arrows and always add up to V_total = 12 V. The checkbox “I_ges” allows you to additionally display the total current as a red arrow.

Where Do You Encounter Voltage Dividers?

Voltage dividers are found in numerous electrical and electronic applications. You often encounter them without even realizing it:

Volume Controls (Potentiometers): A rotary knob on a stereo system or amplifier is a variable voltage divider. Turning the knob changes the resistance ratio and thus the signal voltage – adjusting the volume continuously. In the animation, the potentiometer is selected as the default component. The slider on the left represents the rotation angle α. The coordinate system on the right shows the linear relationship between rotation angle and resistance value R_Pot: a larger rotation angle yields a proportionally larger resistance.
Temperature Sensors: An NTC thermistor is often combined with a fixed resistor to form a voltage divider. Since the NTC’s resistance changes with temperature, so does the output voltage – allowing a microcontroller to measure temperature. Select “Thermistor” using the radio buttons at the bottom of the animation to simulate this case. The slider then represents the temperature ϑ, and the coordinate system shows the non-linear relationship between temperature and resistance R_Ther. Observe how the voltage distribution behaves differently compared to the linear potentiometer.
Light Sensors: A light-dependent resistor (LDR) works in a similar way. Combined with a fixed resistor, it forms a voltage divider whose output voltage depends on the ambient brightness – the basis of many dusk-to-dawn switches. In the animation, this behavior can be simulated by selecting “Fotodiode” via the radio button. The slider then controls the light intensity E, and the non-linear characteristic curve of R_Photo is displayed in the coordinate system on the right.
Logic Level Shifting for Microcontrollers: Many sensors operate at 5 V logic levels, while modern microcontrollers (e.g., ESP32) only tolerate 3.3 V. A simple voltage divider with two resistors can reduce the signal voltage to a safe level. The basic idea can be replicated in the animation: Select the potentiometer and set the resistance values so that V_RPot reaches the desired target value – the displayed voltage changes in real time.

When switching between the four component types in the animation, you will notice that the circuit diagram in the center adapts: the circuit symbol of the second component changes accordingly. For the transistor, an additional base current I_b is shown as a red arrow, since the transistor is controlled via this current.

Loaded and Unloaded Voltage Dividers

The formula shown above strictly applies only to the unloaded voltage divider – that is, the case where no current is drawn from the output. In practice, however, a load (a consumer circuit) is almost always connected to the output.

What Happens Under Load?

When a load resistance R_L is connected in parallel with R₂, the two resistors form a parallel combination. The total resistance of this combination is less than R₂ alone:

\[ R_{2,total} = \frac{R_2 \cdot R_L}{R_2 + R_L} \]

R_2,total: total resistance of the parallel combination
R₂: resistance of the second resistor in the voltage divider
R_L: load resistance

Since R_2,total is smaller than R₂, the output voltage V_out drops compared to the unloaded case. This effect is commonly referred to as “voltage sag.”

When Can the Load Be Neglected?

A common rule of thumb: if the load resistance R_L is at least ten times greater than R₂, the output voltage deviates only slightly from the ideal value. The smaller R_L is relative to R₂, the more the voltage drops – and the less suitable a simple voltage divider becomes as a voltage supply.