Combination Circuits

What is a Combination Circuit?

At this point, you should have learned about Series and Parallel Circuits and the properties they each have to make them unique. However, in real life, we seldomly have a true series circuit or a true parallel circuit. Life is messy, so why shouldn't circuits be. The majority of the electronics that we use in our day-to-day lives have a set of combination circuits. This means that the circuit will have and demonstrate traits from both Series and Parallel circuits. It is important for us to understand how to break down and analyze combination circuits to check for current flow, voltage drops, power ratings, and more. Looking at the image on the right, we can see just how quickly a combination circuit can get complicated.

A combination circuit is an electrical circuit that combines elements of both series and parallel circuits. It contains components that are connected in a combination of series and parallel configurations. The purpose of using a combination circuit is to take advantage of the benefits offered by both circuit types.

In a combination circuit:

Series Components: Some components are connected in series, meaning they are connected end-to-end, forming a single pathway for the electric current. The same current flows through each component in the series. The total resistance in a series portion of the circuit is the sum of the individual resistances.
Parallel Components: Other components are connected in parallel, meaning they are connected side by side, providing multiple pathways for the electric current to flow. The voltage across each parallel component is the same, and the current is divided among the parallel branches based on their resistances.
Voltage and Current: The voltage across the series portion of the circuit is divided among the series components, while the voltage across the parallel portion is the same for all parallel branches. The current through the series components is the same, while the current through each parallel branch depends on its resistance.
Resistance Calculation: Calculating the total resistance of a combination circuit can be more complex than in a simple series or parallel circuit. The total resistance depends on the arrangement and values of the resistors in both series and parallel sections of the circuit. The overall resistance can be determined using a combination of series and parallel resistance rules.

Combination circuits are commonly found in practical electrical systems where different components need to be connected in various configurations to achieve desired functionality. Examples include residential electrical wiring, electronic devices, and complex circuitry in industrial applications. Understanding and analyzing combination circuits require knowledge of both series and parallel circuit principles and their interconnections.

Combination Circuits come in all different shapes and Sizes

Series Circuits nested in Parallel Branches

Series Circuits into Parallel Branches

Combination Circuit using Nodes

Combination circuit analysis

Once you have identified a combination circuit, you have to break it down and simplify it to do a primary circuit analysis. Basically you will need to do everything you have done with Series and Parallel Circuits but together and in a logical order. This may include finding out total resistance, total current, current over each leg, any voltage drops on individual components, power consumption, and more. To start this process, let us first review the basic rules of Series and Parallel Circuits. This will come in handy as we continue our analysis.

Combination Circuit Analysis Example

Using the following Circuit, let us do a full circuit analysis based on what we already know with Ohm's Law, the Power Formula, Voltage Drops, and Current flow theory. For this, let's Identify Total Voltage, Total Power, the Voltage Drops over each component, Current over each component and through each leg, Power over each component, and Total Current.

Let us first do the easy part and identify everything that we can based on the original schematic.

From here, the next logical step would be to find total resistance, the current through each resistor, and total current. For this, we will have to simplify our circuit. Simplifying a circuit means that we will combine what we can to bring it down to as few components as possible. The schematic will end up looking different but will be functionally the same when we follow all the rules of Series and Parallel Circuits. In general, the rule of thumb is to start combining components furthest from the power source. In this case, that means combining R2 and R3 to be one resistor value, usually referred to as R' (R prime). For that, we will need the Parallel Resistance formula.

The formula for combining R2 and R3 will look like this:

R' = 1/(1/10000 + 1/100000)

↓

R' = 1/.00011

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R' = 9090.9 Ω

We know this is probably correct because the total resistance of the new R' is less than the smallest resistor value which was R2, 10000 Ω.

From here, we just have to add the two resistors that are now in Series using the Series Circuit Resistance formula. This will look like this:

Rt = R1 + R' Rt = 1000 + 9090.9 Rt = 10.9 KΩ

We can redraw the circuit so that is just one resistor with the circuit's total resistance. At this point, you have found Total Resistance, but you can also find the Current total using Ohms Law. That will look like the following:

It = Vt/Rt It = 9V/ 10090.9 It = .00089 A or .89 mA

If we remember our Series and Parallel Circuit rules, we will know that the Total Current is the same as the current in a Series circuit because all components in a series circuit flow through the same path. Knowing this, any component in our circuit that is in series will also have a .89 mA current. This applies to R1.

We can now add the new numbers to our table.

From here, we can do the voltage drops on each component that is in Series which in this case, is just R1. The voltage drop formula for R1 will look like this:

V(R1) = 9(1000/10090.9) V(R1) = 9(.099) V(R1) = .891 V

Since R2 and R3 are in parallel and the only component in their branch, the voltage drop over R2 and R3 are the full available leftover voltage after the voltage drop of R1.

As proof to check that our currents are correct, our individual parallel currents should add up to the total current.

It = .00089 = I2 + 13 = .00081 + .000081

The proof checks out, so we are correct.

From here we can fill out the table again. All we have left is I2 and I3, and all the Powers. To find the remaining current we can use Ohm's Law where I=V/R. Let us find the following two remaining currents:

I2 = V'/R2 I2 = 8.109/10000

I2 = .00081 A or .81 mA

I3 = V'/R3 I3 = 8.109/100000

I3 = .000081 A or .081 mA

Finding Power over each component is simple now. Reminder, the formula for Power is P=IV. So, simply multiply the current through each component times the voltage drop over each component. This will look as follows:

P1 = I1(V1) = .00089(.891) = .00079 W or .79 mW

P2 = I2(V2) = .00081(8.109) = .0065 W or 6.5 mW

P3 = I3(V3) = .000081(8.109) = .00065 W or .65 mW

From here, the Total Power consumed by this circuit is just all the individual powers consumed by the components added together. For this it would be:

Pt = P1 + P2 + P3 = .00079 + .0065 + .00065 = .00794

After this, you would just check that no individual power exceeds the power rating of an individual component and that your total power doesn't exceed the limits of your power source.

Our final Filled out table

Our table of the basic circuit analysis values has been filled out. Using the same logic as demonstrated on this page, you could do the same thing for any breakdown of any resistive circuit no matter how complex. Just be sure to remember the rules of Series and Parallel circuits and refer to them as needed when breaking down and simplifying a circuit analysis.

Exercises

Special Note:

Before building any circuit, you should do a brief circuit analysis to make sure the circuit is safe to build. To do this, you can use the sample Electronics Job Sheet to do a rough inspection of the voltage, current, and resistance. This sheet will also allow you to check for power and compare that to a component's power safety rating as well as voltage drops for individual theory. The sheet also has space to sketch a quick breadboard diagram, schematic drawing, and PCB layout.

Adding Resistors in a Combination Circuit

For the following circuit, you will see that it will require you to use both series and parallel resistance formulas. Remember to add the series circuits of each branch first and then do the total parallel circuit resistance. You will see directions to do this in the steps below.

It is good practice to sketch the schematic on the Electronic Job Sheet before moving forward.

For the circuit shown above on the breadboard, fill out the following table below. Assume R1 is the resistor closest to the positive terminal of the battery. In this case, R2 would be the resistor in series with R1. Use this pattern to move forward. Remember, there is no power on the circuit when measuring resistance.

The breadboard circuit you are going to build below is a 9V Battery with a safety diode then five resistors in combination. Starting from the battery and going down each branch of the parallel circuit, the resistor color bands in order are:

R1: Yellow- Purple- Brown- Gold

R2: Red- Red- Brown- Gold

R3: Brown- Black- Yellow- Gold

R4: Brown- Black- Red- Gold

R5: Blue- Gray- Orange- Gold

After adding the series circuits within each branch of this combination circuit, redraw what the circuit would look like as a purely parallel circuit. Label the “new” resisters as R1’ and R3’ and label their values on the schematic. This will help you see the current flow and resistance total of each branch each step of the way.

Now using the parallel formula, add the three resistors to find the total resistance.

Calculating and Measuring Current

For the following circuit, you will notice that you have two parallel branches of a resistor and LED in series. In this section, you will build this circuit and measure the current to find the current of each leg. Using Ohm’s Law and the techniques we used above, you will be able to find the resistance of each LED in the circuit.

When measuring current, you have to physically interrupt the circuit with the multimeter. Notice how in the new circuit to the right that the resistors have been taken out of series with the LEDs and are now connected by having to physically flow through the multimeters. With power on and the circuit interrupted by the multimeter, set the meter to read mA DC and record the current.

Current over Leg A: ________ Current over Leg B: ________

Remembering the properties of parallel circuits, we know that the entire 9V of the battery will go over each leg of the circuit. To be accurate, measure the voltage of your battery.

Measured Voltage of Battery: ___________________

Now that we have the currents and voltages of each leg, we can complete Ohm’s law to find the total resistance of each leg. Using Ohm’s law, find the total resistance of Leg A and Leg B.

Rt of Leg A: ________________ Rt of Leg A: ________________

Working with the total resistance of each leg, we should measure the resistance of each resistor with our multimeter to stay consistent.

R1 Measured: __________________ R2 Measured: __________________

The breadboard circuit you are going to build below is a 9V Battery with a safety diode then two resistors and LEDs in combination. Starting from the battery, the resistor color bands in order are:

R1: Yellow- Purple- Brown- Gold

R2: Brown- Black- Orange- Gold

Note: The LEDs can be any color for this experiment, they just should be the same color to ensure ideal results.

Subtract the corresponding resistor from each leg’s total resistance to find the resistance of the LED in each leg. LEDs have a resistance that changes depending on the current flow so they should not be the same.

LED1: _____________________ LED2: ____________________

Calculating Power

Using the series circuit below, we will calculate power. In order to calculate power, we will need the circuit’s voltage and current. Remember, the formula for Power is P = IV. From above, you know that we need to physically interrupt the circuit with the multimeter to measure current. We also know from our Series Circuit’s rules that we will only have one current for the whole circuit.

Using the circuit to the right as an example, power the circuit and measure total current for the circuit.

It: ____________________

Now, to check power over each component of the circuit, we can measure the voltage drops over each component

Across the safety diode. V1________________

Across the 470-ohm resistor. V2________________

Across the LED V3________________

Now to calculate power:

P1 = It_________ * V1___________ = ________________

P2 = It_________ * V2___________ = ________________

P3 = It_________ * V3___________ = ________________

From here you can add the three powers together to get this circuit's total power

Pt: _______________

You can also take the total current and multiply it by the total voltage to check your work. The total power should be the same plus or minus a reasonable percent error.

The breadboard circuit you are going to build below is a 9V Battery in series with a safety diode, resistor, and LED. Starting from the battery, the resistor color bands in order are:

R1: Yellow- Purple- Brown- Gold

R2: Brown- Black- Orange- Gold

Note: The LEDs can be any color for this experiment, they just should be the same color to ensure ideal results.

Combining it all Together

Using all the information you have learned from the page above and exercises on the Series and Parallel pages, do a complete circuit analysis of the following circuit. You need to fill the chart with the nominal or measured values for each component and requirement. What this will allow you to do is find the voltage over, the current through, and the resistance of every component in the circuit- for instance, without looking up its chart, and LEDs resistance will remain a mystery most of the time while using it because most multimeters cannot read resistance when current is flowing and LEDs have variable resistance based on current. Using what we know from the Series and Parallel rules plus the past exercises you will be able to do a full circuit analysis on simple series, parallel, and combination circuits.

Note:

On this table, you will find things greyed out. This is because you cannot measure the resistance of the LED and from there we cannot measure total resistance. Voltage drops cannot be calculated without the total resistance of the branch. The Current total is the sum of the individual branches and therefore cannot be measured using a conventional multimeter. Finally, power does not have a readout on most multimeters and therefore can only be calculated.

As you continue your calculations, stay consistent in which ones you use.

These exercises can also be found in the Ohm's Law, Power, Series. and Parallel Packet if you want this printed. For more exercises that continue the application of building on a breadboard and measuring voltage, current, and resistance in circuits, look at our Electronic Projects page- this page will dive deeper into different electronic components and their functions. If you need help with more foundational skills, consider looking at our Series Circuit and Parallel Circuit page.

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