Similar to Kirchhoff’s Law, the Voltage and Current Divider rules help us calculate the related voltages or currents in a circuit. There is much more to this but if you are in a rush here are the equations to use:

Summary of Voltage & Current Divider Circuits and Equations

Important:

  • In Parallel branch
    • Voltages are the same
    • Current splits (not equally, but based on the resistance in the branch)
  • In Series (2 resistors after each other)
    • Voltage drops are different (depends on the value on the resistor)
    • Currents are equal

Current Divider

  • In the above circuit the current splits between R1, R2 and R3.
  • As the resistors are in parallel, the voltage is equal across them.
    • Therefore, only the resistance value determine how much of the current flows across a particular resistor.
    • From Ohm’s Law, the larger the resistor is, the less current flows in that branch.
  • The current that flows in the circuit is equal to the current flows out from the circuit.

Let’s see two cases:

Case 1: Find the current in each branch in a 2 resistor circuit.

2 branch current divider circuit
  • 10A flows into a circuit
  • The current splits in 2
  • The red arrows indicate the voltage drop across the resistors.

    • Note, they point to the higher potential. We know the direction as the current flows from the positive terminal (highest potential)

This is a simple circuit so it has some easier methods to calculate the currents. To see them all, let’s cover 3 solutions:

Solution 1: Using the Current Divider equation:

Solution by using the equation for a two branch Current Divider circuit

Solution 2: Using a simplified equation:

that is only true when we are calculating with 2 resistors. Note that we have R2 in the nominator, yet we are finding I1.

Simplified equation for 2 branch Current Divider circuit

 

The calculation as follows:

Calculation by using the simplified equation for a 2 branch Current Divider circuit

Solution 3: Using intuition:

  • R1 is twice the value of R2, therefore,
  • By Ohm’s Law, twice the current flows through R2 (smaller resistance -> more current)
  • 1/3 of the total current will flow through R2.
  • The total current is 10A. The third of 10A is 3.33A
  • So the current in the R2 branch is 3.33A

Case 2: Find the current in each branch in a 3 resistor circuit.

Three branch Current Divider circuit

As before, the current divides between the branches. Let’s use 3 different approaches to find each current:

I1: Using the equation:

Solution for I1 buy using Current Divider equation in a 3 branch circuit

I2: By using Ohm’s Law:

we calculate the voltage drop across R1. Since VR1 = VR2, and we know the value of R2, we can calculate the current instead of using the long equation:

Equal voltage drops across each resistor
Finding I2 by using Ohm's Law in a 3 branch Current Divider circuit

I3: By intuition:

R3 has twice the resistance of R2, therefore, there will be half the current flowing in it.

If you compare two resisters in parallel where one resistor is 2x the value of the other, there will be half the current flowing through the larger resistor than through R1.

optional reading: Success in Electronics book by Tom Duncan
NEXT TOPIC: The Superposition Theorem