Practical Applications of Voltage Divider in Engineering (Part 1): Measuring Internal Resistance
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Time to read 6 min
Intro
In our previous blog, we introduced the voltage divider through its basic calculation formulas and some common pitfalls observed in lab experiments, along with simple methods to address them. That discussion was mainly at the level of classroom learning and textbook-style practice. In this article, we take a step further into engineering applications. Rather than focusing on equations alone, we will explore several real engineering scenarios that build on top of the voltage divider rule.
Quick Recap of Voltage Divider Fundamentals
A voltage divider is simply two (or sometimes multiple) resistors in series, scaling an input voltage into a smaller output. The textbook formula is straightforward:
What matters in practice is that the divider never operates in isolation. Once a load is connected, the effective resistance changes, and the ideal ratio no longer holds. Real design must consider resistor tolerance, power rating, thermal stability, and the effect of input and output impedance. Ignoring these quickly turns a neat formula into misleading results in actual circuits.
With that foundation in mind, let’s move beyond the basics and examine how voltage dividers appear in real engineering scenarios.
Internal Resistance: Theoretical Analysis
Every real voltage source, from a battery to a benchtop function generator to a microcontroller pin, has a finite internal resistance. Textbooks may treat sources as ideal for simplfied analysis and modeling, but in practice this resistance determines how much the output voltage will drop once a load is connected.
What Is Internal Resistance
From the outside, the internal resistance determines how much the source voltage drops when a load is connected. An open-circuit measurement shows the ideal voltage, but once current is drawn, the internal resistance causes a measurable voltage sag. This model is closely related to the Thevenin equivalent, a fundamental concept in circuit theory. In fact, the internal resistance we are estimating here is simply the Thevenin resistance of the source as seen from its output terminals.
DC Internal Resistance Model and Calculation
For open circuits where no current is drawn, the output voltage of the source simply equal to the ideal condition. When a load RL is connected, the internal resistance forms a voltage divider with the load and the output voltage can be expressed as:
For very small RL (heavy load), most of the voltage drops across the internal resistance, a phenomenon known as the loading effect. This is why voltmeters and oscilloscopes are built with very high input impedance, so their presence minimally disturbs the circuit.
Key points engineers note in practice:
Large RL: Vout ≈ Videal (open-circuit condition).
Small RL: Output voltage drops significantly, revealing the effect of Rint.
The slope of Vout vs. current drawn can be used to estimate Rint.
Other Considerations: Frequency and Impedance
While the DC analysis above is straightforward, real signal sources often come with a mixture of DC and AC components. For AC signals running at higher frequencies, internal resistance becomes part of a more general concept: source impedance. Like resistance, the impedance is still expressed in ohms, but unlike pure resistance, it is frequency dependent, often including capacitive or inductive elements that change the effective impedance as frequency varies.
In practical engineering, this frequency-dependent source impedance must be considered in measurement and design. Proper impedance matching between the source and the load is critical in high-frequency circuits, communication links, and instrumentation systems. Without it, signal reflections, distortion, or significant loss can occur, making accurate measurements or reliable data transfer impossible.
Experimental Measurement of Internal Resistance
Introduction to the Experiment
To move beyond theory, we carried out a direct measurement of internal resistance using the Zoolark device. Zoolark provides a feature called DC Reference , which outputs a stable DC voltage intended for biasing purposes. Because this output stage is not designed to drive heavy loads, it offers an excellent case study for characterizing source internal resistance. Our goal is to determine this resistance by applying different loads and observing how the output voltage responds.
Zoolark is an essential device in Lab-On-The-Go kit
Experimental Setup and Data Collection
The DC Reference output was connected through a potentiometer acting as a variable load. By gradually adjusting the resistance, we reduced the load step by step and recorded the corresponding output voltage. A digital multimeter measured the voltage directly across the load, while the potentiometer setting was noted for each point.
In this setup, I set the output voltage to 3.00V, and using the voltmeter, the open-circuit voltage as measured is 2.994V, which can be treated as ideal condition.
As shown in the video, I connected a variable resistor to the output. As the load increased, the output voltage gradually dropped until, at a certain point, it collapsed abruptly. This is related to the semiconductor output stage characteristics , where the device enters a nonlinear region and can no longer sustain the nominal voltage. For estimating internal resistance , the measurement should focus on the linear operating region before this collapse, where the output voltage decreases predictably with load.
Based on the measurement data, the output voltage of the Zoolark DC Reference showed a gradual drop under increasing load. In the linear region, the slope of the curve can be used to estimate the effective internal resistance. Using the voltage divider relation:
the calculated value is approximately 10 Ω , consistent across multiple points before the nonlinear collapse region.
Discussion and Analysis
The measurement confirms that the Zoolark DC Reference has an internal resistance of roughly 10 Ω. This value is small compared to typical kilohm-level loads but large enough to cause noticeable voltage sag once the load drops below a few hundred ohms. For practical use, this means the DC Reference is excellent for biasing and reference-level tasks, but unsuitable as a general-purpose supply for driving lower-resistance loads.
From an engineering perspective, this highlights two important points.
Every real source has internal resistance. For pure DC cases, this resistance can be effectively modeled and estimated using the voltage divider relationship, as demonstrated in the experiment.
For AC sources, internal resistance generalizes to source impedance. At higher frequencies, impedance becomes frequency-dependent and often requires more complex considerations such as impedance matching to ensure accurate signal transfer and minimal loss.
Extending to DC Bias in Transistor Circuits
The same reasoning about internal resistance and loading directly applies to DC biasing in transistor circuits . A voltage divider is often used to set the base or gate voltage, but the transistor’s input resistance effectively loads the divider, shifting the bias point if not properly designed. Understanding how to model this interaction is critical for stable amplifier operation and predictable switching behavior.
In our upcoming discussion, we will explore how voltage divider biasing works in practice, and how to choose resistor values that balance stability with power consumption. This is one of the core experiments included in our Fundamental Analog Circuit Kit, which provides the hardware and guided labs for students and hobbyists to practice these concepts hands-on. If you are interested, the kit is available for purchase through our store.
Some FAQs
Why does every voltage source have internal resistance?
Even highly regulated supplies and precision references rely on semiconductor devices, pass elements, and feedback loops. These components inherently limit how much current can be delivered, which appears externally as a finite internal resistance.
How can I quickly estimate internal resistance without plotting a curve?
A simple method is to connect a load that reduces the open-circuit voltage to about half. At this point, the load resistance approximately equals the internal resistance. While less precise than curve fitting, this rule of thumb is often useful for quick checks.
What role does internal resistance play in AC signal integrity?
In AC systems, internal resistance extends to source impedance, which can be reactive and frequency-dependent. Impedance mismatches between source and load cause reflections, distort waveforms, and reduce power transfer, especially in high-frequency communication circuits.
How does this concept connect to transistor biasing?
When using a voltage divider to bias a transistor, the input resistance of the base or gate effectively loads the divider. This is conceptually identical to measuring internal resistance: if the divider is not designed with enough margin, the bias point shifts and circuit stability suffers.
Can buffering completely eliminate loading effects?
Yes. Adding a buffer such as an op-amp voltage follower isolates the source from the load, making the effective output impedance nearly zero. This approach is common in precision reference circuits and sensor front-ends.
Daniel Cao
Daniel Cao is the founder of EIM Technology, where he creates hands-on, beginner-friendly electronics education kits that blend practical hardware with clear, structured learning. With a background in engineering and a passion for teaching, he focuses on making complex concepts accessible to learners from all disciplines.
