There are so many concepts when it comes to learning physics and electrical energy. One of the most important and fundamental concepts is the current divider. Due to its importance, there is a need to understand and get a good grasp of this concept before one move to more advanced concepts.
Here, we will explain the definition of the current divider circuit, Ohm’s law (which is closely related to the concept), current divider rule as well as current divider formula and three different examples to make it easier to understand. We will also explain some other related concepts at the end of the article.
What Is It?
Let’s start with the definition.
What is a current divider? Put it simply, it is a simple linear circuit. What makes it different is that the amount of input and output current it produces. In this simple circuit, the input current is divided into fractions, thus resulting in a smaller output current than the input current.
The current division here refers to the current splitting between the divider’s paths. The more paths are there, the smaller an output current is. This is why an output current is only a fraction of the input current. The currents in this circuit always divide in a way that minimizes the total energy expended.
Current Divider Circuit
The term current divider and parallel circuit are often interchangeable. This is due to such the circuits’ ability to divide its total current into smaller, fractional parts. In a parallel circuit, all of its components have interconnected terminals that share the same two end nodes.
Different Currents Moving Across ‘Paths’
As the circuit is divided, there are at least two ‘paths’ or branches for current to pass through. Although the branches share the same amount of voltage, the currents may not be divided equally for each branch as a branch can have a higher current than the others.
According to Ohm’s law, the voltage of a circuit can be found by multiplying the circuit’s current and resistance or impendence. Or if put it into a formula: V = I x R, where V is voltage, I is current and R is resistance. If any two quantities (regardless which ones) are known, the third one can be found.
Since the concept of current divider involves circuits, including the DC circuit, it is related to Ohm’s law. The law explains the relationship between voltage, current and resistance, all of which can be found in parallel circuits. You will see how close the relationship between the two in the current division formula section.
Current Division Rule
The current division rule states that the current passing through any parallel branch of a circuit is equal to the total current multiplied by the ratio of an opposite branch resistance to the circuit’s total resistance. With this rule, a branch’s current can be found if the total current and other branches’ resistance values are known.
Current Division Formula in Brief
If current division rule is turned into a formula, it looks like this:
IBranch = Is (RTotal / RBranch), where
- IBranch is the current passing through a certain branch
- Is the current source
- RTotal is the total value of resistance
- RBranch is the value of resistance of a certain branch
That is the formula of the current divider in brief. The main take here is that the current is allocated to each branch. The value of the allocated current may or may not be equal to each other.
Detailed Explanation of Current Division Formula
Previously, we explained the current divider rule and how it looks like when it is turned into a formula. It is, however, a brief explanation. The following is a more detailed explanation, which explains the logic behind and how the IBranch = Is (RTotal / RBranch) current division formula comes from.
Suppose there is a parallel circuit with two parallel branches. The current that passes through the first branch is I1 while the current that passes through I2. How does the current division formula look like? The following is the answer.
Start with Ohm’s law, which says V = I x R
Since V is the same across all branches in a parallel circuit, that means
The current that passes through the first branch is equal to the voltage divided by the resistance in the first branch. If put into formula: I1 = V / R1 and I2 = V / R2
To find the total resistance, the resistance of both branches are multiplied then divided by the total value of them. So the current division formula to find the total resistance is R = (R1 x R2) / (R1 + R2)
Continuing the current divider formula, the I = V / R can be written like the following
I = V (R1 x R2) / (R1 + R2)
Keep in mind that V is the same across all paths, which means
I = I1 x R 1 = I2 x R2
We can put the above into the I = V (R1 x R2) / (R1 + R2) formula
I = I1 x R1 x (R1 + 2) / (R1 x R2) which equals to I1 / R2 x (R1 + R2)
Likewise with the I2 and R2
I = I2 x R2 x (R1+R2) / (R1 x R2) which equals to I1 / R1 x (R1 + R2)
From this, we get the current division formula to find I1 and I2
I1 = I x (R2 / (R1 + R2)) and I2 = I x (R1 / (R1 + R2))
Put it differently, IBranch = Is (RTotal / RBranch)
Thus, according to the current divider rule, a current in a certain branch in a parallel circuit is equal to the total current multiplied by the ratio of the opposite branch resistance value to the total resistance value.
We have explained the concept and the formulas of current divider. The examples below show how the concept and formulas are put into practice.
Example #1: A circuit with 2 resistors parallel to each other
Suppose a current divider has two branches each has a resistor parallel to each other. The first resistor is R1 and the second is R2. R1 has a resistance of 4Ω and R2 has 8Ω. The input current is 6A. How much is the currents that flow to each branch? How much is the voltage?
First, let’s calculate the I1 or the current that pass through the first branch
The formula is:
I 1 = ITotal x (R2 / (R1 + R2), which means
I1 = 6 x (8 / (4+ 8))
I1 = 6 x 8 / 12
I1 = 4A
The current that pass through the first branch is 4A
And the formula to find the I2 or the current that pass through the second branch is
I2 = ITotal x (R1 / R1 + R2), which means
I2 = 6 x (4 / (4+8))
I2 = 6 x 4 / 12
I2 = 2A
Alternatively, since the input current is fractioned into two, we can know the amount by subtracting the known current. It goes like the following
If I1 is known, then I2 = ITotal – I1
I2 = 6 – 4
I2 = 2A
If I2 is known, then I1 = ITotal – I2
I1 = 6 – 2
I1 = 4A
As for the voltage, the amount is the same all across the branches. In other words, V1 = V2
V1 = I1 x R1 is equal to V2 = I2 x R2
V1 = 4 x 4, V2 = 2 x 8
V1 = 16, V2 = 16
This proves V1 = V2
Example #2: A circuit with 3 resistors parallel to each other
Suppose a circuit has 3 resistors. The first resistor (R1) has a resistance of 2Ω, the second resistor (R2) has a resistance of 4Ω, and the third resistor has a resistance of 8Ω. How much is the current flowing through each resistor? How much is the voltage?
The formula to find I1 is
I1 = ITotal x ((1 / R1) / (1 / R1 + 1 / R2 + 1 / R3))
I1 = 14 x ((1/2) / (1/2 + 1 / 4 + 1 / 8))
I1 = 14 x 8 / 14
I1 = 8A
To find I2,
I2 = 14 x ((1/4) / (1/2 + 1 / 4 + 1 / 8))
I2 = 14 x 8 / 28
I2 = 4A
To find I3,
I3 = 14 x ((1/8) / (1/2 + 1 / 4 + 1 / 8))
I3 = 14 x 1 / 7
I3 = 2A
Alternatively, since ITotal is the sum of all three currents
ITotal = I1 + I2 + I3
14 = 8 + 4 + I3, therefore I3 = 14 – 8 – 4
I3 = 2A
For the voltage,
V = I x R and V1 = V2 = V3
V1 = I1 x R1, which means V1 = 8 x 2 = 16V
V2 = I2 x R2, which means V2 = 4 x 4 = 16V
V3 = I3 x R3, which means V3 = 2 x 8 = 16V
Example #3: A circuit with 4 resistors
A current divider has 4 resistors: R1, R2, R3, and R4 where R1 has a resistance of 12Ω, R2 24Ω, R3 16Ω and R4 8Ω. The total amount of current passing through the circuit is 15A. How much is the current flowing through each resistor? How much is the voltage?
To find a given current, the formula is
Ix = ITotal x ((1 / Rx) / (1 / R1 + 1 / R2 + 1 / R3 + 1 / R4)), where x is the current being sought
To find I1,
I1 = ITotal x ((1 / R1) / (1 / R1 + 1 / R2 + 1 / R3 + 1 / R4))
I1 = 15 x ((1 / 12) / (1 / 12 + 1 / 24 + 1 / 16 + 1 / 8))
I1 = 15 x ((1 / 12) / (15 / 48))
I1 = 15 x 4 / 15
I1 = 4A
To find I2,
I2 = 15 x ((1 / 24) / (15 / 48))
I2 = 15 x 2 / 15,
I2 = 2A
To find I3,
I3 = 15 x ((1 / 16) / (15 / 48))
I3 = 15 x 3 / 15
I3 = 3A
To find I4,
I4 = ITotal – I1 – I2 – I3
I4 = 15 – 4 – 2 – 3
I4 = 6A
The amount of the voltage is the same across all resistors, which means
V1 = V2 = V3 = V4
As such, only one calculation is needed. The formula is
Vx = Ix x Rx, where x is the resistor chosen.
If we choose resistor 1 or R1, then the formula becomes
V1 = I1 x R1
V1 = 4 x 12
V1 = 48
Related Concepts: Voltage Divider
The current divider is also related to the voltage divider. The former is about the division of current in a parallel circuit whereas the latter is about the division of voltage in a series circuit. According to voltage divider rule, the voltage is divided into fractions while the current is the same.
If put into a formula, voltage divider goes like this
Starting with Ohm’s law, where I = V / R or I = E / R
Keep in mind that since it is a series circuit, the formula becomes
I = E / (R1 + R2) and E1 = I x R1
Since the current is the same all across, E1 = I x R1 and E2 = I x R2
From here, we get
E1 = (E x R1) / (R1 + R2) and
E2 = (E x R2) / (R1 + R2)
This means in a series circuit, the voltage across a certain resistor equals to the multiplication of the total voltage and said resistor value divided by total resistance values in the circuit.
To recap, a current divider is a parallel circuit that has the same amount of voltage while the current is divided into fractions for each of the parallel branches the circuit has. A voltage divider, on the other hand, is a series circuit that has the same amount of current while the voltages are fractioned.