# How to Solve a Resistor Series Parallel Circuit with Practical Demonstration

Have you ever tried to learn to solve a series parallel circuit but weren’t sure if you were getting the right answers? That’s quite understandable because most places you learn to solve this type of circuits, its mainly just play with numbers and formula. But electrical and electronic circuits are not easy to visualise, and only one small mistake will lead you to a completely wrong string of results if you have nothing to compare your results with. In this blog, I’ll show you how to solve a resistor series parallel circuit with a practical demonstration, that way, when you solve this type of circuit, you will have some idea of its real outcome.

## Here’s the Series Parallel Circuit Question

I will also wire this circuit using our DC pracbox to show you the difference between calculated and real values and discuss the reasons behind the discrepancies.

## How to Begin Solving a Series Parallel Circuit

Always begin by labelling the circuit with all its parameters. Even better would be to redraw it and then mark it. This will give you a bird’s eye view of the circuit and the information you are trying to find.

Next, you should visualise the current path to understand which parts of the circuit are series and which are parallel. Do this while keeping the simple rules of current flow in mind, like higher resistance means less current and lower resistance means more.

At this stage, you should also think about how the voltages will drop across the components using basic rules of electricity. For example, voltages are same parallel parts of a circuit, and higher resistors will have a higher voltage drop in series circuits.

By now, you should have a good idea of how the circuit will behave; and now we can proceed to solve it.

**What to solve first?**

I would say that this is probably the biggest concern a learner has when they are learning to solve a series parallel circuit. All these numbers and multiple questions and none of it seems straight forward. Most people just find what they can with what they have and then worry about what they’re actually looking to find. Although, this is an easy method when you’re just learning but keep in mind that there is a more systematic approach to solving all calculation questions, which we will discuss in another post.

For now, let’s find what we can with what we have been given, and looking at the circuit, you may notice that we have all resistor values so we could start by finding the equivalent resistance of this circuit. We can also call this the total resistance, but the equivalent resistance is technically a more appropriate term.

## Find Equivalent Resistance in the Series Parallel Circuit

To find the equivalent resistance or total resistance of a circuit, you need to understand the resistor network first; understand what resistors are in series or parallel.

By looking at the circuit, we can be quite sure that resistors B and C are in series. Another thing that will become apparent is that resistors B and C together are in parallel with resistor D. Since resistor A connects in a way that all the circuit current must go through it, we can safely say that it’s in series with the rest of the network.

But how to start? You can’t do anything with resistors A and D till we have the total resistance for B and C because it’s the smallest network in this circuit.

Rule: Solve the smallest network first.

Here are the solution and a comparison with a real circuit in the DC pracbox

The calculated value of the equivalent resistance is slightly different from the measured value in the demonstration, and that could be because of the tolerances of the resistors, terminations, connections and even meter leads.

## Find the Total Current

With the information you have now, including the equivalent resistance, it should be easy to find the total circuit current IT, which needs total voltage and total resistance in Ohm’s law

Here are the solution and a demonstration

The calculated value of the current is slightly different from the measured value in the demonstration, and that’s because the practical total resistance is different from what we had calculated.

## Find the Power Dissipated by Resistor A

We had figured out earlier that the current through resistor A is the total circuit current so using that we can calculate the Power dissipated by it.

Here’s the solution; this is one of the parameters we were looking for in the question.

## Find the Voltage Drop Across Resistor D

If we go back one step when we were finding the total resistance, you may realise that the resistor A is in series with the rest of the network. In a series resistor network, the voltage is shared between the circuit components based on their resistances. Keeping this in mind, let’s see the solution and a demonstration of voltage drops for this circuit

The voltage across resistor D was also one of the parts of the question.

## Find the Current Through Resistor C

The small exercise of visualising current flow that we did before we started solving the question will come in handy here. The total current travels from point P and through resistor A, after which it splits into two parts – one goes to resistor D and the other goes to resistors B and C. Since the resistances of D and the network B and C are different, the current will also be different.

Here are the solution and the practical demonstration on the DC pracbox

We just solved the remaining part of the question.

## Conclusion

Solving a resistor series parallel circuit can be daunting when you’re learning it for the first time. I would encourage you to see all circuits for what they are and how they might behave in real life rather than just solve it theoretically. Once you understand the behaviour, over time and with practice, solving these types of circuits will become easier and easier.

I hope this post has helped you understand the process of solving a resistor series parallel circuit and understanding its practical effects from the demonstration. Please let us know in the comments below if you have a different way of solving this type of circuits.

Thanks for dropping by.

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## About the Author

#### Husnen Rupani

I help electrical training organisations increase learner engagement by designing innovative training equipment. I have a saying "Electricity - you cannot see, you cannot hear it, but by the time you feel it, it may be too late." My main aim is to turn this black magic that we call electricity into something that people can understand.

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