A junction is a place where three or more current paths meet.

The junction rule: The total current coming into a junction equals the total current going out from a junction.

Consider the following situation, where a 2 W resistor is in parallel with a 3 W resistor. A current I comes into the junction before the resistors, splitting into two currents I₂ through the 2 W resistor and I₃ through the 3 W resistor.

The junction rule tells us that I = I₂ + I₃

What fraction of I passes through the 2 W resistor?

1. 1/3
2. 2/5
3. 1/2
4. 3/5
5. 2/3

The correct answer is 3/5, which we can prove. Let's make our method more general by calling the two resistors R₂ and R₃. We know resistors in parallel have the same potential difference across them, so:

DV = I₂R₂ = I₃R₃

Combine this with the junction equation: I = I₂ + I₃

Therefore I₃ = I - I₂

Substitute this into the first expression:

I₂R₂ = (I - I₂) R₃

I₂R₂ = IR₃ - I₂R₃

I₂ (R₂ + R₃) = IR₃

I2

=

IR3 R2 + R3

With our values we get:

I2

=

3 5

I

The junction rule is actually a conservation law in disguise. The junction rule is equivalent to the Law of Conservation of ___________?

1. Energy
2. Momentum
3. Mass
4. Charge
5. Current

Charge. The total charge flowing into a junction equals the total charge flowing away from a junction.