### Parallel Circuits

A parallel circuit allows for more than one path for current to flow. We have the same two loads from the series circuit below, but we have two paths now for electrons to flow. Each pathway for current to flow is called a branch.

In a parallel circuit, if the light (load) in branch 1 were to be faulty, the light (load) in branch two would still function as there’s another pathway around the faulty load to take for the electrons to flow.

#### Rules of a Parallel Circuit

• Rule 1: The voltage across each branch of a parallel circuit will be the same as the applied voltage.

V total = V1 = V2 = V3 = …

• Rule 2: The total current of a parallel circuit is the sum of the current in each branch.

I total = I1 + I2 + ….

I total = 1A + 1A

I total = 2A

We have a total of 2A split between 2 different loads in this circuit.

The amount of current that travels through each branch will not necessarily be the same because the resistance of the load in each branch will dictate the current flow. The higher the resistance in the load, the less current flow

• Rule 3: The total resistance in a parallel circuit is less than any of the individual resistances.
##### Calculating Total Resistance With 2 Resistors:

Calculating resistance total with only two resistors in parallel is a bit easier than calculating for 3 or more.

Example:

Resistor 1: 12Ω

Resistor 2: 24Ω

R total = R1 x R2 / R1 + R2

R total = 12Ω x 24Ω / 12Ω + 24Ω

R total = 288Ω / 36Ω

R total = 8Ω

##### Calculating Total Resistance with 3 or More Resistors:

The formula for calculating 3 or more resistors is a little different and there’s a bit more to it.

Example:

Resistor 1 = 5Ω

Resistor 2 = 20Ω

Resistor 3 = 10Ω

Resistor 4 = 1Ω

R total = 1/ (1/R1 + 1/R2 + 1/R3 + 1/R4)

R total = 1/ (1/25Ω + 1/20Ω + 1/10Ω + 1/1Ω)

R total = 1/ (.04Ω + .05Ω + .1Ω + 1Ω)

R total = 1/1.15Ω

R total = .84Ω

#### Calculating Current in Each Branch

Now that we know the total resistance of this circuit to be 8Ω, calculating current in each branch comes down to basic Ohm’s Law.

Step 1: We need to calculate the current for the whole circuit.

I = E / R

I = 12V / 8Ω

I = 1.5A

The total current through the circuit is 1.5V. We know that each branch will have different current since the resistive loads are different sizes.

Step 2: Calculate the current for each branch separately.

Resistor 1: 12Ω

I = E / R

I = 12V / 12Ω

I = 1A

Resistor 2: 24Ω

I = E / R

I = 12V / 12Ω

I = .5A

Step 3: Confirm individual current calculations.

We can confirm our individual branch calculations are correct by adding them together and comparing them to our total circuit current calculation.

I total = I1 + I2 + ….

I total = 1A + .5A

I total = 1.5A

1.5A is exactly what we calculated in step 1.

#### A Broken Path Will Not Stop Current Flow

If a path for current to flow is broken, current will continue to flow in other paths that are still available.