Series-Parallel Circuits- Part 1

It's been a long time ago when I posted my last topic about Electric Circuits.  Though its very difficult to have time to write a topic for this blog, this site will always be alive for you. I would like to thank first those who have subscribed to this blog.

Well, let's talk about another basic topic about Basic Electrical Engineering. This is about Series-Parallel Circuits. For those who are just new with this site, you can surely catch up with my previous post at Electrical Engineering Syllabus that I've provided last time.

Circuits can be connected into complex circuits consisting of three or more resistors. One part of the circuit is in series and the other part could be connected in parallel. This connection is called the Series-Parallel Circuits.

There are two types of series-parallel connections: the first one is the resistance in series with a parallel combination and the other one is the series in which the parallel combination have a series of resistances. Let's see the figure below for better understanding of this theory.

a. This is a series resistances with a parallel combination.

b. This is a series resistance and series of resistances in a parallel combination.

Take for example you have three lamps to be connected in a source of a battery. There are two ways that you can connect it. The first one is that: connecting the first lamp connected in series to the parallel combination of the second and third lamp. The second one is that: first and second lamp is connected is series then connect it parallel to the third lamp.


How to Simplify a Series-Parallel Circuit Connection?

In dealing with series-parallel connection, there's nothing something new formula to be use here except for concept of Ohm's Law.

In terms of simplifying a circuit, all you need to do is to start first with the most complex part before you get the overall resistances of the entire circuit. Take the following steps below as your guide. This is what I've always follow when I was still a student.

1. First, redraw the circuit in a most comprehensive way if necessary. Some circuits looks like complicated at first glance, but if you will redraw it equivalent to the original circuit, you could easily deal with it.
2. Start to simplify the circuit in the complex part. In the parallel combination with branches consisting of two or more resistors in series, start to simplify them by adding its value.

3. Then using the formula of the parallel resistances, get the value of resistances of parallel parts of the circuit.

4. Then, combined the resistances of the entire circuit.

Is it clear? Ok let's proceed...

Let's take a sample figure 2 below:

Using the steps above:

1. You don't need to redraw the circuit above, since it is obviously where to start simplifying the circuit.

2. Simplify the resistance of D and E first using the equivalent resistances in parallel formula. Then, add the combined resistances of D and E to C using the resistances in series formula.

3. Since you already get the value of combined resistances for D and E to C. Then, you may now get the combined resistances of B to D, E and C using resistances in parallel.

4. Get the overall resistance Rt = Ra + R(combined resistances of B, C, D and E).

Now you get the clear understanding of series-parallel circuits. On my next post, I will show you more illustrative examples which were already given in previous Electrical Engineering Board Exams.

Cheers!