Circuits that consist of voltage dividers allow many voltage levels to be generated from a single voltage source. This source may be a voltage of +5V, +12V, -5V, or -12V, or it may be a negative voltage with respect to ground (0V). A dual supply, consisting of positive and negative voltages such as ±5V or ±12V, is another option.
Voltage dividers are sometimes referred to as potential dividers. This is so because the volt, the unit of measurement for voltage, represents the potential difference between two locations in a circuit.
Functions of Voltage Dividers
A voltage divider is a basic, passive circuit. It makes use of the idea that voltage decreases across parts that are connected in series. One such example is the potentiometer, which is a variable resistor with a sliding contact. Its terminals can be biased to provide an output voltage that is proportional to the sliding contact's position.
Additionally, we can build voltage dividers with inductors, capacitors, and fixed resistors. These components are ideal since they have two terminals and can be wired in series.
Using Resistive Divider
Two resistors connected in series is all that is needed to create the most common type of voltage divider. With this straightforward configuration, you can calculate the voltage across each resistor using the voltage divider rule.
Resistive Voltage Dividers
Consider an electrical path that has two resistors, R1 and R2, connected one after the other (as shown in the above figure). The current that flows through both resistors must be the same since electricity can only travel through this chain in one way. A voltage drop (I * R) is produced across each resistor by this current.
Kirchhoff's Voltage Law (KVL) and Ohm's Law are two scientific laws that may be used to determine the voltage drop across each resistor in this chain if a power source (VS) is connected to it.
We can calculate the voltage drops by determining the current (I) passing through the circuit, as shown below.
VS = VR1 + VR2 (KVL)
VR1 = I * R1 and VR2 = I * R2
Therefore, VS = (I * R1) + (I * R2)
∴ VS = I(R1 + R2)
Thus, I = VS / (R1 + R2)
According to Ohm's Law, the current flowing through the series network is just I = V/R. Given that both resistors share the same current (IR1 = IR2), we can determine the voltage dropped across resistor R2 in the series circuit above as follows:
IR2 = VR2 / R2 = VS / (R1 + R2)
∴ VR2 = VS [R2 / (R1 + R2)]
In the same manner we can calculate for resistor R1 as given below:
IR1 = VR1 / R1 = VS / (R1 + R2)
∴ VR1 = VS [R1 / (R1 + R2)]
Solving a Voltage Divider Problem
As shown above, consider a circuit consisting of two resistors: R1, which has a resistance of 10 ohms (Ω), and R2, which has a resistance of 20 ohms (Ω). These resistors are connected in a straight path, one after the other. This indicates that the current going through the circuit must pass through both resistors. Additionally, we have a power supply that supplies a steady 6 volts DC (direct current) voltage throughout the whole series connection.
What we want to find:
Current (I): Because the resistors are connected in series, the amount of electrical current (measured in amperes, A) that flows through each one will be equal.
Voltage drop (V): Keeping in mind that a voltage drop is created when current passes through a resistor, what voltage drop (measured in volts, V) will occur across each resistor?
RT = R1 + R2 = 10 + 20 = 30 Ω
I = VS / RT = 6 / 30 = 0.2 Amps or 200 mA
VR1 = I * R1 = VS [R1 / (R1 + R2)] = 6[10 / (10 + 20)] = 2 Volts
VR2 = I * R2 = VS[R2 / (R1 + R2)] = 6[20 / (10 + 20)] = 4 Volts
In a voltage divider circuit, each resistor generates a voltage drop (I * R) that is proportional to resistance. The voltage drop that is produced over the same current increases with resistance. We can figure out which resistor will have a greater voltage drop using this relationship.
Consider a voltage divider, for example, where R1 = 2V and R2 = 4V (these numbers are voltage drops, not resistor values). In this case, the voltage drop across the bigger resistor (8V) would be greater than that across the smaller resistor (4V). This makes sense because Ohm's Law (I = V / R) states that a higher resistance makes it "harder" for current to flow, resulting in a bigger voltage drop.
This behavior is consistent with Kirchhoff's Voltage Law (KVL), which dictates that the total voltage provided in a circuit must match the sum of the voltage drops around a closed loop. In our case, the supply voltage is 12V (drop across R1 + 8V across R2), proving KVL.
The voltage divider rule states that the voltage will divide uniformly across resistors with identical values (R1 = R2). The voltage divider ratio would therefore be 50%, meaning that each resistor would contribute equally to the total resistance, and each resistor would experience a voltage drop equal to 50% of the source voltage.
Variable Outputs and Sensors
Voltage dividers are not restricted to fixed voltage drops. We may use a potentiometer in place of resistor R2 to provide a variable voltage output. This component functions similarly to a sliding contact variable resistor (wiper). The ratio of the two resistances in the circuit varies as you move the wiper. This in turn regulates the output voltage (VOUT) by controlling the voltage drop across the potentiometer (formerly R2).
There are many kinds of variable resistors:
- Potentiometers: Frequently employed in manual adjustments.
- Trimmers: Tiny, movable resistors used to fine-tune circuits as they're being constructed.
- Rheostats: Variable resistors, which are less frequent in contemporary electronics, are used to manage higher currents.
- Variacs: Special transformers with adjustable output AC voltage.
Voltage Dividers with Sensors
There is more we can do with this idea! We can employ a sensor that modifies its resistance in response to external factors in place of a fixed resistor (R2). An illustration of this would be an LDR, which decreases resistance in response to increased light levels. The output voltage (VOUT) will vary in accordance to the light intensity if an LDR is used in lieu of R2. This enables us to design circuits that respond to variations in light.
Other sensor types follow similar principles:
Thermistors: Resistance varies with temperature.
Strain gauges: Strain gauges vary in resistance when manually pulled or squeezed.
By combining voltage dividers and sensors, we may create circuits that respond to a variety of environmental factors like as light, temperature, and pressure.
The two voltage division formulas above must technically be related to one another because they both refer to an identical source current. Therefore, the voltage dropped across each specific resistor in a series network made up of any number of individual resistors is given as follows:
Formula for Voltage Dividers
VR(X) = VS(RX / RT)
The formula indicates the voltage drop (VR(x)) across a certain resistor (RX) in a series circuit. The meaning of each section is as follows:
VR(x): Voltage drop across an individual resistor (x) in the series.
RX: The resistor's specific resistance value, expressed in x.
RT: The total resistance (sum of all resistances) in the series circuit.
This formula is accurate because in a series circuit, the voltage drop across each resistor is determined by the value of its resistance. The higher the resistance, the greater the voltage drop experienced by the same current running through it.
Solving a Voltage Divider Problem (Example#2)
Imagine we have three resistors:
- Resistor 1 (R1) with a resistance of 3k ohms (Ω)
- Resistor 2 (R2) with a resistance of 6k ohms (Ω)
- Resistor 3 (R3) with a resistance of 9k ohms (Ω)
The resistors in question are connected in series, which means that any current that goes through the circuit has to travel through each resistor one after the other. The complete series has been connected to a power source that maintains a constant voltage of 18 volts.
What we have to find:
- Total Resistance (RT): The total resistance of the circuit when all three resistors are combined.
- Current (I) is the amount of electrical current (which is expressed in amperes, A) that runs via each resistor.
- Voltage Drop (VR1, VR2, VR3): The voltage drop (in volts, V) across each resistor.
Solving the Problem:
RT = R1 + R2 + R3 = 3k + 6k + 9k = 18k
I = VS / RT = 18 / 18000 = 0.001 Amp = 1 mA
VR1 = VS(R1 / RT) = 18(3000 / 18000) = 3 Volts
VR2 = VS(R2 / RT) = 18(6000 / 18000) = 6 Volts
VR3 = VS(R3 / RT) = 18(9000 / 18000) = 9 Volts
Kirchhoff's Voltage Law states that the total of the voltage drops across the three resistors should equal the supply voltage (KVL). Therefore, the total voltage drops equals: VT = 3 V + 16 V + 9 V = 18.0 V, which is the same as the supply voltage, VS, and is therefore accurate. We again observe that the voltage drop is biggest when the resistance is largest.
Accessing Different Voltages in a Voltage Divider
Consider a series of resistors that are linked to a power supply (VS). We may access various voltage levels at specific points throughout this chain, such as A, B, C, D, and E.
The sum of all the values of each individual resistor makes up the chain's total resistance (RT). Let's assume that the total resistance in this case is 15,000 ohms (Ω). When supplied by the voltage source (VS), the overall resistance creates a limitation on the quantity of current that may flow through the circuit.
Using the voltage divider rule, we may obtain the voltage drop across each resistor. According to the tapping locations they connect to, these voltage drops are given names, such as VR1 for the voltage drop between points V and A, VR2 for the drop between B and C, and so forth.
Every tapping point's voltage is measured in relation to ground (0 volts). Therefore, VDE is the voltage at point D. However, the voltage at position C is more fascinating. It is equal to VR3 + VDE, the total of the voltage dips across the two resistors (R3 and R4) that came before it. Stated differently, the voltage across the previous resistors in the chain causes the voltage at point C to build up.
We may produce a sequence of voltage drops that supply different voltage levels from a single source by carefully choosing resistor values. Keep in mind that because the power source's (VS) negative wire is connected to ground (0V), all of the voltage points in this example will be positive.
Consider it similar to a voltage ladder. Every voltage drop across a resistor functions as a ladder step. The voltage level at various places along the chain may be controlled by selecting the appropriate resistor sizes for each step.
Solving a Voltage Divider Problem Example#3
Assume the voltage divider circuit we studied before is linked to a 15-volt DC power supply. In a "no-load" situation, when there is no additional load attached, what voltage would we obtain at each tapping point (A, B, C, D, and E)?
To calculate these voltages, we may apply the voltage divider rule, as shown below.
RT = R1 + R2 + R3 + R4 = 8k + 4k + 2k + 1k = 15k
VR1 = VAB = VS(R1 / RT) = 15(8000 / 15000) = 8 Volts
VR2 = VBC = VS(R1 / RT) = 15(4000 / 15000) = 4 Volts
VR3 = VCD = VS(R1 / RT) = 15(2000 / 15000) = 2 Volts
VR4 = VDE = VS(R1 / RT) = 15(1000 / 15000) = 1 Volts
2) Next, we determine the voltage output at noload between points B and E.
RT = R1 + R2 + R3 + R4 = 8k + 4k + 2k + 1k = 15k
VBE = VS[(R2 + R3 + R4) / RT] = 15[(4k + 2k + 1k) / 15k] = 7 Volts
Voltage Divider Circuit having both Positive and Negative Outputs
Although the majority of voltage dividers provide outputs that are referred to ground (0 volts), there are circumstances in which you require both positive and negative voltages from a single source.
Circuits in electronics, such as the power supply unit (PSU) in a computer, frequently operate like this. Different voltage levels, such as -12V, +3.3V, +5V, and +12V, may be supplied by a PSU with respect to a common ground terminal.
How it Works:
Resistors are used in conventional voltage dividers to produce a voltage drop from a single source. We may regulate the amount of voltage drop across each resistor by adjusting these resistor values. The reference point for the voltage measurement is crucial when it comes to positive and negative voltage dividers.
Non-Grounded vs. Ground Circuits:
Standard Voltage Divider: In this case, a common reference point is zero volts. With respect to this ground, every voltage output is positive.
Positive and Negative Voltage Divider: In this case, we may not utilize ground as a reference. Instead, voltage dips across strategically arranged resistors produce both positive and negative voltages with respect to a central point which may not be ground (0V).
Solving a Voltage Divider Problem with both Positive and Negative Voltage Outputs
Given Information:
- Desired output voltages: -12V, +3.3V, +5V, and +12V
- Total supply voltage (VS): 24V DC
- Total power (P): 60 watts (for unloaded circuit, which means that no additional components are drawing current)
What we need to find:
- Resistor values (R1, R2, R3, and R4)
Solving the Problem:
P = V * I
∴ I = P / V = 60 / 24 = 2.5 Amp
R1 = (VA - VB) / I = (12 - 5) / 2.5 = 2.8 Ω
R2 = (VB - VC) / I = (5 - 3.3) / 2.5 = 0.68 Ω
R3 = (VC - 0) / I = 3.3 / 2.5 = 1.32 Ω
R4 = (VD - 0) / I = 12 / 2.5 = 4.8 Ω
In contrast to the previous examples, this voltage divider is not referred to ground (0V). Instead, we changed the zero-voltage point, resulting in both positive and negative voltages from the same power source. This is a typical method for producing multiple voltage levels in circuits.
Think of it this way: Consider a voltage divider circuit as a seesaw. In a standard divider, one side is always grounded (0V). We've raised one side of the seesaw slightly to establish a new reference point that's not on the ground. This allows us to generate both positive and negative voltage outputs with respect to the new reference.
In this particular instance, point D achieves the necessary -12V level when compared to the new reference point, which serves as our common ground. Each of the four voltage outputs (+12V, +5V, +3.3V, and -12V) are monitored using this new reference point.
References: Voltage Divider