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.

2 loads in series Vs. 2 loads in a parallel circuit

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/ (1/5Ω + 1/20Ω + 1/10Ω + 1/1Ω)

R total = 1/ (.20Ω + .05Ω + .1Ω + 1Ω)

R total = 1/1.35Ω

R total = .74Ω

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.

What this means on a service call

A parallel circuit gives each load its own path, and the voltage is the same across each branch. That changes what a failure means. If one branch opens, the other branches can still work. The light in branch 1 can fail while the light in branch 2 still runs, because current still has a path around the faulty load.

On a service call, that independence changes the diagnosis. A dead load does not prove that power is gone. Check that branch first. A working load proves voltage is present at the common points, but it does not prove every branch is good. Test each branch on its own before you call the circuit good.

Numbers and measurements you will see

The numbers below all come from the 12V example with a 12 ohm resistor and a 24 ohm resistor. Use the three rules to check each other. Voltage stays the same, currents add, and total resistance falls below any one branch.

• Voltage is the same, 12V. Each branch sees the full applied voltage. Do not split the voltage between branches as you would in series.
• Total resistance is 8 ohms. In the example, 12 ohms and 24 ohms in parallel give 8 ohms total. That total is lower than either branch alone.
• Total current is 1.5A. In the example, 12V divided by 8 ohms gives 1.5A for the whole circuit.
• Branch 1 current is 1A. In the example, 12V divided by 12 ohms gives 1A.
• Branch 2 current is 0.5A. In the example, 12V divided by 24 ohms gives 0.5A. The higher resistance branch carries less current.
• Check by adding branches. In the example, 1A plus 0.5A gives 1.5A, which matches the total current. In the first example in this post, 1A plus 1A gives 2A total.

A common mistake

The most common mistake is to use series thinking in a parallel circuit. Do not expect the current to be the same in each branch, do not add the resistances to get the total, and do not split the voltage between branches. In parallel, voltage is the same, resistance total falls, and branch currents differ when branch resistances differ.

A second mistake is to measure the total current and assume each branch carries that much. In the example, the total is 1.5A, but no branch carries 1.5A. Branch 1 carries 1A and branch 2 carries 0.5A. Measure each branch on its own, and add the branch currents to check the total.

Check it in the field

1. Check the applied voltage across the branches. Each branch should show the same voltage. Record the voltage and the test points.
2. Measure current in each branch separately. Clamp one insulated conductor for one branch only. Keep hands clear of bare parts, and record each branch reading.
3. Add the branch currents together and compare the sum with the total current. In the example, the branch currents must add to 1.5A. If they do not, recheck the test points and the meter.
4. If a branch shows 0A while voltage is present across it, check that branch only. With the power off, and the circuit proved dead, check continuity through the load and wiring in that branch until you find the break.

Do resistance and continuity checks with the power off. Prove the circuit dead with a voltage test first. Do not clamp more than one conductor at once when you want a branch reading. Stop and get help if you are unsure about the power state.

Related posts

These posts belong together.

• Voltage, current, and resistance summary: a short recap of voltage, current, and resistance together.
• Voltage: the push that makes current flow, and how to read a voltage test.
• Current (amps): what flow means, and how to check it without guessing.
• Resistance: what opposition to flow means, and why a load must have resistance.
• Series Circuits: one path for current, with the same current through each part.
• Ohm’s Law: how voltage, current, and resistance relate, with worked examples.