Completed Voltage Division Rule Formula

Voltage division rule is very famous because it is used for voltage divider circuits. Voltage divider circuit has very wide applications in electrical systems. This circuit works with a simple method and comes with a very simple calculation. You will often find or even use this circuit for many applications. A voltage divider circuit is able to produce a specific percentage of the maximum voltage from the circuit to our liking.

Voltage divider circuit shares the same circuit as a series circuit. The current in series circuit is always the same for every resistance it passes through. As opposed to parallel circuits, the voltage drop for each resistor is different from each other depending on its resistance. The total current in the series circuit is divided by total resistance in the circuit.

Voltage Division Rule

The voltage across each resistor can be calculated with the famous Ohm’s Law. It states that the voltage across a resistor is the product between the total current passing that resistor and its resistance.

Before we go on to the voltage division rule, we must understand how voltage, current, and resistance are used to determine the output. We can use the simple example below.

Given that a circuit has n resistor,

voltage division rule

The total resistance of the series circuit will be:

    \begin{align*}R_{eq}&=R_{1}+R_{2}+...+R_{n}\end{align*}

The total current of the series circuit will be:

(1)   \begin{align*}I=\frac{V}{R_{eq}}\end{align*}

The voltage across the R1 will be:

(2)   \begin{align*}V_{1}=I\times R_{1}\end{align*}

The voltage across the R2 will be:

(3)   \begin{align*}V_{2}=I\times R_{2}\end{align*}

The voltage across the Rn will be:

(4)   \begin{align*}V_{3}=I\times R_{3}\end{align*}

Substituting (1) into (2) makes

    \begin{align*}V_{1}=V\times\frac{R_{1}}{R_{eq}}\end{align*}

Substituting (1) into (3) makes

    \begin{align*}V_{2}=V\times\frac{R_{2}}{R_{eq}}\end{align*}

Substituting (1) into (4) makes

    \begin{align*}V_{n}=V\times\frac{R_{n}}{R_{eq}}\end{align*}

Where:

Vn = voltage drop across the n-th resistor

Rn = resistance of the n-th resistor.

The sum voltage drop across the n series resistors is equal to the ratio of total current divided by equivalent resistance of the resistors. From the formula above we conclude that,

The voltage drop across an n-th resistor is the product between input voltage and the resistance of the n-th resistor divided by equivalent series resistance.

Voltage Division Rule Formula Example

For a better explanation, observe the circuit example below:

1.Circuit below consists of 2 resistors with different resistance.

voltage division rule

The total resistance or equivalent resistance is

    \begin{align*}R_{eq}&=R_{1}+R_{2}\\&=3+2\\&=5\Omega\end{align*}

The total current is

    \begin{align*}I&=\frac{V}{R_{eq}}\\&=\frac{5}{5}=1A\end{align*}

The voltage drop across the R1 will be

    \begin{align*}V_{1}&=I\times R_{1}\\&=V\times\frac{R_{1}}{R_{eq}}\\&=5\times\frac{3}{5}\\&=3V\end{align*}

The voltage drop across the R2 will be

    \begin{align*}V_{2}&=I\times R_{2}\\&=V\times\frac{R_{2}}{R_{eq}}\\&=5\times\frac{2}{5}\\&=2V\end{align*}

2.Circuit below consists of 3 resistors with the same resistance.

voltage division rule

The equivalent resistance will be:

    \begin{align*}R_{eq}&=R_{1}+R_{2}+R_{3}\\&=3+3+3\\&=9\Omega\end{align*}

The total current will be

    \begin{align*}I&=\frac{V}{R_{eq}}\\&=\frac{9}{9}=1A\end{align*}

The voltage drops for each resistor will be

    \begin{align*}V_{1}=V_{2}=V_{3}&=V\times\frac{R_{1}}{R_{eq}}\\&=9\times\frac{3}{9}\\&=3V\end{align*}

Since the resistances are the same, the voltage drops for each resistor are the same.

3.Circuit below is one we call a voltage divider circuit. We only add a terminal on one resistor to get desired voltage.

voltage division rule

Get straight to the point, the Vout will be

    \begin{align*}V_{out}&=V_{2}\\&=V\times\frac{R_{2}}{R_{1}+R_{2}}\\&=5\times\frac{3}{5}\\&=3V\end{align*}

Frequently Asked Questions

What is the voltage division rule formula?

Voltage division rule formula for n-th resistor is
Vn = Vx(Rn/Req)

How do you use the voltage division rule?

Voltage division rule is used for series circuits such as voltage divider circuits. It calculates the voltage drop of a desired resistor in a series circuit.

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