Contents
What is a Voltage Divider?
A Simple Voltage Divider Circuit
A simple voltage divider features two resistors in a series arrangement. Primarily, a divider acts as a voltage regulator. It ensures that there is a voltage drop across a circuit. Hence, the output voltage is of a lower potential difference than the supply voltage.
The difference in the voltage levels (voltage drop) fundamentally relies on the values of the two series resistor values. Also noteworthy, the electric current on either end of the divider remains the same.
The general voltage divider equation is as follows:
The Voltage Divider Equation.
The denominators in the equation represent the sum of the two resistance values. Meanwhile, the numerator R2 represents the divider resistor over which you measure the output voltage.
The Voltage Divider Rule Formula
Resistive Voltage Divider
Circuit Diagram
Such a voltage divider features a series combination of two resistors. We can also calculate the voltage drop across each resistor via the Voltage Divider Rule.
Let’s take two resistors, R1 and R2, in a series arrangement. They’ll have a common currency across each resistive element as long as they are in a Loop arrangement. Hence, we’ll use the ohms law to calculate the voltage drop across each element.
Let’s take a supply voltage Vs. Enters via the first resistor. Using the Ohms law and Kirchhoff’s Voltage Law (KVL), we can evaluate the specific voltage drop for each resistor.
According to Kirchhoff, Voltage Law Vs. = Voltage of R1 + Voltage of R2.
But, R1 voltage= I x R1 and R2 voltage = I x R2 since one current flows across both resistors.
Hence, Vs = I x R1 + I x R2
Next, we can factor out the load current I to obtain;
Vs = I( R1 + R2) and the current, I = Vs ÷ (R1 + R2).
Voltage Drop Across R2
Remember that in this circuit, the flow of current is in series. Hence, from Ohm’s law, I = V/ R.
But, R1 current equals R2 current. Now, the current across R2 is as follows.
Deductively, the voltage across R2 equals:
Voltage Drop Across R1
First, we’ll deduce the equation for current across R1
Hence, the voltage across R1 equals:
A Negative and Positive Voltage Divider
A Voltage Divider Circuit Schematic
In the former voltage divider circuit described above, we base our output voltages on one zero-voltage ground point. However, a wide range of applications requires using a single source voltage supply to generate positive and negative voltages.
For instance, a computer power supply unit (PSU) will generate varying output voltages such as +5V, +3.3V, +12V, and -12V. The PSU outputs the above voltages from a common reference ground terminal.
Voltage Divider Example
Question: Consider you have an unloaded voltage divider circuit with a 24V DC supply voltage and 60 Watts. Calculate the Resistors R1, R2, R3, and R4 that you would require to obtain -12V, +3.3V, +5V, and +12V voltage levels, respectively.
Hint: Use Ohm law.
Solution:
This circuit’s zero-voltage ground reference point will produce negative and positive voltages. However, the voltage divider network remains in place despite the split of voltages.
Hence, we need a common reference point, D, from which we should measure the voltages. In our case, the lowest point is negative 12V, which serves as the reference voltage point for the ground.
Therefore, using the equation, Power equals Voltage x Current, We can calculate the common circuit current.
P= Vx I, I =P ÷ V = 60 ÷ 24 = 2.5A.
Hence, the resistor’s values are as follows:
Capacitive Voltage Dividers
Circuit Diagram
An electronic circuit with capacitive voltage dividers features capacitors connected in a series arrangement with an AC power supply. A capacitive voltage division circuit steps down high input voltages to output a low voltage output signal.
You’ll often find capacitive voltage dividers in basic circuit display devices such as smartphones.
While a resistive voltage divider circuit uses AC and DC supplies, a capacitive divider will only operate on a sinusoidal AC supply. Fundamentally, the voltage division calculation across the capacitors relies on the capacitor’s reactance (XC). The reactance is a function of the AC supply’s frequency so that DC supplies won’t work.
Capacitive Reactance Formula
π (pi) = a numeric constant of 3.142
C = Capacitance in Farads, (F)
ƒ = Frequency in Hertz, (Hz)
Xc = Capacitive Reactance in Ohms, (Ω)
Also, for two capacitors in series, XCT = XC1 + XC2.
Hence, the voltage across the respective capacitors is as follows:
VC1 = Vs(XC1/ XCT)
VC2 = Vs(XC2/ XCT)
But, the overall voltage equation for the output voltage is Vout = (C1/C1+C2).Vin
Inductive Voltage Dividers
Two Inductors
These adjustable voltage dividers create a voltage drop across inductors arranged in series. Primarily, an inductive voltage divider features a single winding/coil with two main parts. Then, you take the output from one end of the windings.
The auto-transformer is an example of an inductive voltage divider.
Notably, the reactance of inductors is close to zero. Thus, using a DC Power source of a low-frequency AC power supply makes the inductor short circuit. For best results, you should use a sinusoidal AC supply.
When calculating the voltage drop, the inductor’s reactance (XL) is the most critical parameter. Like capacitive inductance, the inductive reactance also varies with the supply voltage change.
Inductive reactance formula
The inductive reactance is given by: 
Whereby,
π (pi) = a numeric constant of 3.142
XL = Inductive Reactance in Ohms, (Ω)
L = Inductance in Henries, (H)
ƒ = Frequency in Hertz, (Hz)
Inductive Voltage Divider Circuit
Below is a circuit diagram for a simple inductive divider circuit.
From the two Inductors, L1 and L2, we can calculate the voltage across them.
So, the Individual Inductive reactances will be as follows.
We can also find the total Inductive reactances using the formula below.
Next, the following formulas are handy in evaluating the voltage across each of the Inductors.
Also, note that the voltage drop across each inductor is directly proportional to their respective reactances.
Conclusion
A voltage divider is crucial in splitting the input voltages to give several different outputs. We’ve also described several voltage divider circuits and their essential qualities. For more insights, Talk to us at any time.
