Learn How the Voltage Divider Works with Rules and Calculations

We use voltage dividers regularly in electronics, sometimes without even knowing it. But how do voltage dividers work? In this article, we will learn about the voltage divider rule, how to calculate the resistance value, and how to use it in actual circuits.

A voltage divider is a very basic part of electronic circuit building. But sometimes we may forget or overlook it. So brushing up and relearning about a voltage divider can be very beneficial. As for beginners, knowing about it definitely helps you build or understand circuits.

What is a Voltage Divider?

First off, let’s understand the basics of a voltage divider circuit. It is a passive circuit that divides or reduces voltage among its components.

The simplest and most basic consists of two resistors connected in series to the power supply, also known as a resistive voltage divider. Some may call it a potential divider, from the voltage being the difference in electric potential.

Also: Learn Zener voltage regulator

In this example, we will refer to the power supply as Vs, and the first and second resistors as R1 and R2, respectively.

According to the series circuit rule, the voltage of the power supply is distributed between R1 and R2. The amount of voltage drops across each resistor is proportional to its resistance. For this voltage divider circuit, what we are concerned with is the output voltage (Vo), which is the voltage across R2.

To better understand how this voltage divider circuit works at different R1 and R2 resistance values, consider these three scenarios:

• R2 is less than R1
  In this case, the output voltage is less than half of the Vs because most of the voltage is across the higher resistance resistor R1.
• R2 is equal to R1
  Now, the Vo is exactly half of the Vs. This is because the voltage is distributed evenly between the two resistors.
• R2 is greater than R1
  The Vo will be more than half of the Vs. R2 has a higher resistance value, so the majority of the voltage is across it. 

In conclusion, if we want the Vo to be greater than half of the Vs, R2 must have a higher resistance than R1. However, for the Vo to be less than half of the Vs, R2 must be lower than R1. 

It sounds simple enough, right? We will also look at the formula and how to calculate the Vo for a given R1 and R2 later.

Recommended: Learn series circuit works.

Reasons to Use a Voltage Divider

Suppose that part of our circuit needs a voltage of 1V; however, the power supply of the circuit is 10V. There are many ways to reduce the voltage from 10V to 1V, but the simplest and easiest way is to use a resistive voltage divider.

It has some downsides, as we will learn about later. However, for the most part, it is the quickest way to get a lower voltage out of a higher voltage source. 

Which is why voltage dividers are often used in common applications such as Zener voltage regulators or reference voltage generators for amplifier circuits.

Voltage Divider Formula

To calculate the exact output voltage (Vo) from given resistance values, we have to use the following formula.

Let’s try this formula out using the same three scenarios from earlier, but now with hypothetical resistance values for R1 and R2. Suppose that Vs = 10V, and we have to find Vo.

• R2 > R1
  Where R2 = 1.5kΩ (1,500Ω), and R1 = 120Ω.

Using the formula, we know that Vo is approximately 9.259V.

• R2 = R1
  Where both resistor is equal: R2 = 2.2kΩ (2,200Ω), R1 = 2.2kΩ (2,200Ω).

In the case that R1 and R2 have the same value, Vs is split evenly between them. Thus, Vo is 5V.

• R2 < R1
  Where R2 = 330Ω, and R1 = 4.7kΩ (4,700Ω).

Applying the formula shows that Vo in this case is just about 0.656V.

Additionally, the formula indicates that the multiplying ratio (R2 ÷ R1 + R2) for Vs is always less than one. The numerator will always be less than the denominator. In other words, for a resistive voltage divider, the output voltage cannot exceed the input voltage.

With that being said, a voltage divider like this one also possesses a few drawbacks.

Drawbacks of Resistive Voltage Divider

The resistive voltage divider, like the one above, is not without flaws. Here are some of its drawbacks and potential solutions to fixing them.

Wasted Energy Without Load

First, energy is wasted when no loads are present. With or without loads, some current from the power supply passes through R1 and R2 to ground. However, when there is no load, all current (I_T) flows through R1 and R2, completing the circuit at ground and wasting the energy.

One simple remedy is to add some kind of switch to control when the circuit functions. And only turns it on when we need the Vo for something.

Limited Output Current

The output current has to pass through R1. So, if we use a very high resistance value for R1, the output current will be almost nonexistent. Furthermore, if the load decides to draw a large amount of current, R1 would heat up or potentially become damaged.

Read first for beginners: How do transistor circuits work

In the case where loads draw too much current, we would see another drawback: the output voltage.

Load-Dependent Output Voltage

If a load across Vo has a very low impedance, current will flow to it rather than across R2. According to Ohm’s law, less current flowing across R2 also means less voltage. This is because, like water, electrical current flows through the path of least resistance, which in this case happens to be the load.

The solution is to use a very high impedance buffer, such as a transistor, an OP-AMP integrated circuit, etc. For example, we could connect a transistor to the output of this circuit. Because the transistor’s base current (IB) is so low, it has little effect on the current flowing through R2, resulting in a far more constant voltage across R2.

Examples of the Voltage Divider Implementations 

The voltage divider in an actual circuit may not just appear in the form of two resistors in series. Here are some examples of how a voltage divider could be integrated into a circuit.

Buffered Output

Buffered output is a way to prevent load-dependent output voltage, as we see above. It sits between the voltage divider circuit and the low input impedance load. The buffer has a very high input impedance; as a result, it has minimal impact on the voltage divider’s output voltage Vo.

The term buffer includes many components, such as transistors, ICs, SCRs, etc. A buffer usually has an amplification effect as well, where it is referred to as an amplifier. But the most common buffers we see are transistors and ICs, so talk about them.

Transistor

We can connect the output of the voltage divider to the base of a transistor. The transistor here functions similarly to a switch. It will turn on (complete the circuit on the load side) when the output voltage Vo reaches a certain point.

However, the base-emitter of a transistor is like a diode, so the voltage across it cannot exceed 0.7V. This effectively limits the Vo to 0.7V. Nevertheless, we can solve this problem by adding another resistor (RE) to the emitter of a transistor. It will increase the Vo as well as the circuit efficiency. Here are a few transistor circuits that use this concept.

OP-AMP

We often use a voltage divider circuit with an OP-AMP to create a reference voltage. This is because an OP-AMP’s input impedance is extremely high, sometimes in the tens of millions. It is especially useful in comparator circuits, amplifier circuits, etc. Below are some circuits that utilize an OP-AMP and a voltage divider in this manner.

Read more: Voltage Monitor circuit  

3 Resistors Voltage Divider 

Sometimes we may also see a voltage divider with three resistors, where there is one additional resistor in parallel with the output resistor (R2). Typically, the primary reason for using this setup is to achieve finer control over R2 resistance.

Considering the circuit above, to find Vo, we must first combine the parallel resistors into one using the parallel circuit rule. Given that Vs = 12V, R1 = 3.9kΩ (3,900Ω), R2 = 220Ω, and R3 = 560Ω. We can find the combined R2 and R3 value, Ro, using the following formula:

From the parallel formula, we can see Ro is about 157.948Ω. Remember that Ro is the same as R2 in the original voltage divider formula, but in this case, Ro is the parallel resistance of R2 and R3 (Ro = R2 ‖ R3).

Now we can apply the voltage divider formula to find the Vo. Note that we replace R2 in the formula with Ro instead. To recap on the value: Vs = 12V, R1 = 3.9kΩ (3,900Ω), and Ro = 157.948Ω.

The approximate result we get is Vo = 0.467V. The key principle in this multiple-resistor voltage divider circuit is to reduce the number of resistors as much as possible. Then, apply the voltage divider formula.

Transducers or Resistance-Variable Sensors

Another use case of a voltage divider is with passive transducers or sensors. Passive transducers are electrical components that change their resistance depending on outside factors or stimuli. For instance, a light-dependent resistor (LDR) may change its resistance based on the light level in its surroundings.

Other resistance-variable sensors include microphones, thermistors, photoresistors, etc. Using sensors like these with another resistor in the form of a voltage divider allows for a finer reading. The output is usually fed into ICs or transistors that interpret the signal.

These passive transducers function like a normal resistor if there are no changes to their stimulus. Therefore, we can put them either before the positive output (R1) or after it (R2). The sensor position will alter the output.

For example, suppose that the sensor in question is an LDR that will have low resistance when in the light and high resistance in the dark.

If we place that LDR before the positive output (R1), the output voltage Vo will be “high” when it is in the light and “low” when it is in the dark. The LDR functions the same as when it is not in a voltage divider circuit.

Whereas if the LDR is placed below the positive output, the output voltage Vo will be “high” when it is in the dark and “low” when in the light. Thus, putting sensors in the below position (R2) inverts their reading properties.

Picking Another Resistor

How do we choose another resistor that would go along with the LDR? For this example, let’s use a 5mm 150VDC max CdS photoconductive cell (LDR). This LDR has a lowest resistance in the light at 10kΩ and a highest resistance in the dark at 1MΩ; we will refer to them as LDRmin and LDRmax, respectively.

Generally, the resistance of R2 should be higher than Rmin while being less than Rmax. So, let’s try using 100kΩ for R2. Now we apply the voltage divider formula for both LDRmin (10kΩ) and LDRmax (1MΩ or 1,000kΩ):

We can see that Vo when LDR is in the light (LDRmin = 10kΩ) is 9.09V, and when LDR is in the dark (LDRmax = 1,000kΩ) is 0.909V. The difference between the lowest and highest Vo is 10 times (9.09 / 0.909 = 10).

But how about we lower the value of R2? Now R2 is equal to 10kΩ and everything else is the same; let’s see the value of Vo.

Now, when LDR is in the light (LDRmin = 10kΩ), Vo is 5V; when LDR is in the dark (LDRmax = 1,000kΩ), Vo is 0.099V. The difference between the two Vo values increases to approximately 50 times (5 / 0.099 = 50.505).

Therefore, if the minimum and maximum resistance of the LDR do not change, lowering the resistance of R2 results in a wider gap between the lowest and the highest output voltage. 

In other words, decreasing the R2 compresses the output ranges, allowing for higher accuracy measurement. However, this is not without a drawback, as we can see that the maximum output voltage decreases from 9.09V to 5V.

For most cases, it is better to use another resistor value that allows for a wide output voltage range. You can either guess the values and then test for the difference, or use the following formula for a rough idea of another resistor’s resistance.

Where R is the resistance of another resistor (R2 in the previous circuit), suppose that LDRmin is 10kΩ and LDRmax is 1MΩ.

This formula can give us a rough idea of which resistance we should try first. It is not a concrete rule; it is better to try for a value that matches the circuit’s needs. Additionally, we can also apply it to other resistance-varying sensors, and not just the LDR. However, will still need the minimum and maximum resistance values, so if the seller does not provide that data, we can measure it ourselves using an ohmmeter.

Potentiometer or Adjustable Ratio

Next are the potentiometers, or adjustable resistors. Potentiometers, like sensors, have variable resistance, but rather than relying on external factors, we can adjust it with physical knobs.

It is especially useful for fine-tuning the output voltage. For this reason, it is often used in devices such as volume knobs, variable power voltage adjustment knobs, radio tuners, etc.

For the most part, it is better to use a potentiometer when building or designing a voltage divider because it allows for adjustment without having to change the resistor. Furthermore, it could also be used to adjust the sensitivity of a sensor, as shown below.

In this example, the LDR is placed at the window to detect when the sun sets, and another resistor (R1) is calculated to be 10kΩ. When the sun sets, the output voltage Vo will be “low.” However, in reality, the Vo turns to “low” an hour before the sun completely sets.

To fix this, we can change R1 to 4.7kΩ and add a 10kΩ potentiometer VR1 in series with it. This allows us to adjust the resistance from 4.7kΩ to 14.7kΩ. Then, we adjust VR1 until the output voltage Vo is “low,” exactly right as the sun sets. We can either leave it as that or find a resistor with a resistance that matches the potentiometer’s resistance and replace it.

Zener Diode Voltage Divider

Generally speaking, a resistive voltage divider does not have the most stable output voltage. But we can greatly mitigate that by replacing the output resistor (R2) with a Zener diode. Given that the voltage level is above the Zener diode’s breakdown voltage, it maintains a stable voltage across itself, and thus, Vo remains stable.

You can read more about how a Zener diode works here:

Our Buy Me a Coffee members can access an extended version of this post. If you’re interested, check it out here: Become a member.
It is one of the ways you can directly support us and our work. We would be grateful if you could consider it.

Get Ebook: Simple Electronics Vol.4