Voltage Divider Rule (VDR) and Current Divider Rule (CDR): in Series and Parallel Circuit

Voltage Divider Rule (VDR) shows how the voltage distributes among different resistor in a series circuit. Similarly, Current Divider Rule (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 series combination has a different voltage drop across it. The individual voltage drop of resistors adds up to source voltage. While the current for series circuit remains same throughout the circuit as discussed earlier.

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

VDR And CDR

Voltage Divider Rule:

In the previous post, series combination, we have solved circuit shown and found the following parameters for the circuit.
V1 = 40 volts
V2 = 80 volts
V3  = 20 volts
Where the source voltage applied to the circuit is 140 volts.

Resistors in series

By looking closely to these number, 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 (VDR). The Kirchhoff’s Voltage Law also state 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 V1 is the voltage drop across the resistor R­1, VT is the total voltage applied to the circuit and R­T­­ is the equivalent resistance of the circuit.

Suppose the above series circuit such that we are interested in finding voltage drop V3 across R3. The VDR formula for V­3 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 is same as we calculated in the previous section using Ohm’s law.

Now, let me find the voltage V2 across the R­2­­. The calculation will be:
$V_{2}=\frac{140 v\times 40\Omega }{70 \Omega }$
$V_{2}=80 v$

Similarly, for V1 the voltage drop across R1 will be:

$V_{1}=\frac{140 v\times 20\Omega }{70 \Omega }$
$V_{1}=40 v$

Voltage Divider Calculator:

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Current Divider Rule:

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 same 140 volts but because of parallel combination the total resistance in 5.7 $\Omega$.

Resistors in parallel

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

Current Divider Formula:

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

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

I1 is the branch current where R­­­1 is connected and we are interested in, IT is the total current provided by the source and R­T is the total resistance of the parallel circuit.

For the circuit given, suppose we are interested in current I3 in R3 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. \(\)

CDR Calculator:

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Total Resistance RT

Resistance Rx

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