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**:

**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 r
**esistors 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.**

**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 2: **U****sing 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**.

The calculation as follows:

**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.**

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

**I1:** **Using the equation:**

**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:

**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

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