Solve Parallel Resistive Circuits

How to Solve Parallel Circuits for Electricians (Example Parallel Math Equations)

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Did you know electricians wire in parallel 99% of the time?! The most important parallel circuit principle to remember is that:

VOLTAGE STAYS THE SAME IN PARALLEL CIRCUITS!

This is very important because whenever you plug in an electrical device, like a TV, toaster, microwave, or computer.. it’s designed to receive 120V. That means wiring in parallel keeps 120V to each plug or light on that circuit!

How to Solve Parallel Circuits for Electricians
You may like How to Solve Series Circuits

How Parallel Circuits Work (Parallel Circuit Principles):

Just like solving series circuits, we need to know electricity principles like Ohm’s Law, and Kirchhoff’s Current and Voltage Laws (also known as Kirchhoff’s rules).

In short, for a parallel circuit, that is:

  • Voltage stays the same
  • Total circuit amperage is the sum of each branch circuit current
  • Total resistance is always LESS than any branch circuit resistance!!!

Parallel is a lot trickier than series circuits, because once you get into combination circuits, you’ll see circuitry equations get very complex and confusing.

If you can remember these parallel circuit principles listed above, (and the series circuit principles), you’ll know the steps to find your answer!

Parallel Circuit Example – for Electricians:

Here’s an example of a parallel circuit equation.

Remember, put T’s at each electrical load to easily solve Ohm’s Law (finding Voltage, Current, and Resistance).

Solve Parallel Circuit Equation for Electricians
Solve Parallel Circuit Equation for Electricians

Here’s the most important things to notice about a parallel circuit, as once you know how to a parallel circuit works, you’ll be able to pass your electrician test no problem!

First, notice how all the voltages are the same; the source, and each branch circuit’s load (R1 and R2). (This is the main reason we use Parallel Circuits so that voltage remains the same for electrical devices).

Second, notice how total circuit current is the sum of each branch circuit! (Total Current is 10A.. R1 is 4A and R2 is 6A!)

Third.. and this one is probably the trickiest.. is the total resistance is LESS than any branch circuit resistance! (Total resistance is only 12Ω.. but R1 is 30Ω and R2 is 20Ω!)

I’ll show the easiest math equation to find total parallel circuit resistance.

How to Find Total Circuit Resistance in a Parallel Circuit

There’s MANY WAYS to find total resistance in a parallel circuit.. but some are pretty tricky to remember. (And when you’re in school, you already have so much on the go!).

This is the EASIEST WAY to find total parallel resistance:

How to Find Parallel Circuit Resistance - Math Equation
How to Find Parallel Circuit Resistance – Math Equation

First, make sure you’re using a scientific calculator, as you’ll need to use brackets!

Then, you simply go:

1 ÷ ( (1/30Ω) + (1/20Ω) ) = 12Ω

The biggest thing to remember is that you have to hit EQUALS .. otherwise you get a decimal number.. instead of 12Ω.

If you try the example above in your calculator, and don’t hit equals, you’ll get: .0833333

As soon as you hit equals.. you get: 12Ω

I’ll type out word-for-word to follow this easy parallel resistance formula step-by-step:

  • 1 divided by
  • Forward Bracket, Forward Bracket
  • 1 divided by (your resistance.. R1 was 30Ω)
  • Close Bracket
  • Plus
  • Forward Bracket
  • 1 divided by (your next resistance.. R2 was 20Ω)
  • Close Bracket, Close Bracket
  • YOU’RE NOT DONE.. you’ll only see a decimal now
  • HIT EQUALS.. and you’ll see 12Ω (for our example)

Conclusion: Solving Parallel Circuits for Electrical Apprentices

I hope that helps you understand parallel circuits.

Here’s other circuit articles that will help you:

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