The Voltage Divider Rule formula (VDR) shows how the voltage distributes among different resistors in a series circuit. Similarly, the Current Divider Rule formula (CDR) shows how current distributes in a parallel circuit.

*VDR and CDR Formulas* are the tools for voltage and current distribution in series and parallel circuits.

Each resistor in a series combination has a different voltage drop across it. The individual voltage drop of resistors adds up to the source voltage. While the current for the series circuit remains the same throughout the divider circuit as discussed earlier.

In a parallel resistor, the voltage across each resistor is the same as the source voltage. But current divides such that the summation of individual resistor current is always equal to source current.

## Voltage Divider Rule Formula:

In the previous post, series combination, we solved the electrical circuit shown and found the following parameters for the circuit.

V_{1 }= 40 volts

V_{2 }= 80 volts

V_{3 } = 20 volts

Where the source voltage applied to the circuit is 140 volts.

By looking closely at these numbers, you will observe that the voltage drop is different from each other and the summation of all of them is equal to the voltage applied to that circuit (source). The question is, how do these voltages relate to each other? The answer is Voltage Divider Rule Formula. Kirchhoff’s Voltage Law also states the same thing.

### Voltage Divider Formula:

According to VDR, it holds the following ratio.

$\frac{V_{1}}{V_{T}}=\frac{R_{1}}{R_{T}}$

Where V_{1} is the voltage drop across the resistor R_{1}, V_{T} is the total voltage applied to the circuit and R_{T} is the equivalent resistance of the circuit.

Suppose the above series circuit such that we are interested in finding voltage drop V_{3} across R_{3}. The VDR formula for V_{3} will be:

$V_{3}=\frac{V_{T} R_{3}}{R_{Eq}}$

By putting the corresponding values, we get:

$V_{3}=\frac{140 v\times 10\Omega }{70 \Omega }$

$V_{3}=20 v$

Note that V_{3} is the same as we calculated in the previous section using Ohm’s law.

Now, let me find the voltage V_{2} across the R_{2}. The calculation will be:

$V_{2}=\frac{140 v\times 40\Omega }{70 \Omega }$

$V_{2}=80 v$

Similarly, for V_{1 }the voltage drop across R_{1} will be:

$V_{1}=\frac{140 v\times 20\Omega }{70 \Omega }$

$V_{1}=40 v$

## Voltage Divider Calculator:

The voltage divider rule calculator is a web-based tool for calculating voltage across resistor Rx. Where Rx is connected in series with another resistor such that their total resistance is RT. The Voltage Divider Formula Calculator calculates the voltage across Rx only based on the voltage divider equation.

## Current Divider Rule Formula:

In the previous post, parallel combination, we have the parallel circuit show and found the following parameters of the circuit.

$I_{1}=7 A$

$I_{2}=3.5 A$

$I_{3}=14 A$

The source voltage is the same 140 volts but because of the parallel combination, the total resistance is 5.7 $\Omega$.

CDR is the counterpart in a parallel electric circuit to VDR in series electric circuits. Based on the above analysis one can observe that the current of different resistors is different being attached to the same voltage source. The reason for this difference is the difference in resistance.

## Current Divider Formula:

CDR formula can calculate the current flow in each resistor. The formula for the current divider is:

$I_{1}=\frac{I_{T}R_{T}}{R_{1} }$

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I_{1} is the branch current where R_{1} is connected and we are interested in, I_{T} is the total current provided by the source and R_{T} is the total resistance of the parallel resistor circuit.

For the circuit given, suppose we are interested in current I_{3} in R_{3} and we know the total current of the circuit from the above calculation. The formula will become for us:

$I_{3}=\frac{I_{T}R_{T}}{R_{3}}$

$I_{3}=\frac{24.5 A\times 5.714 \Omega }{10 \Omega}$

$I_{1}=14 A$

We can also cross-check the calculated currents by Ohm’s law. \(\)

## Current Divider Formula Calculator:

The current divider rule Formula calculator is a web-based tool for calculating current in resistor R_{x}. Where R_{x} is connected in parallel with another resistor such that their total resistance is R_{T}. The CDR Calculator calculates the current in R_{x} only based on the CDR formula.

## Conclusion:

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- The power supply voltage divides fractionally in a series of electrical circuit
- The power supply current divides into parallel electrical circuits partly
- The Voltage divider rule formula is used to find the partial voltage across the individual resistor in a series circuit
- The current divider rule formula is used to find the partial current in the individual resistor in a parallel circuit

the formula is just wrong tho

Which one?