Hey there guys, Paul here from TheEngineeringMindset.com. In this video we're going to be looking at parallel circuits to understand how they work and how to calculate them. There's also some problems at the end of the video for you to try and solve.
So we can connect components of a circuit in either series, parallel or a combination of series and parallel. In these animations we use electron flow, which is from negative to positive. But you might be used to seeing conventional flow which is from positive to negative. Electron flow is what's actually occurring.
Conventional flow was the original theory and it's still taught because it's probably easier to understand. Just be aware of the two and which one we're using. When we place a lamp in series or parallel with a battery, the electrons are going to flow from the negative terminal of the battery, along the wire, through the lamp and then to the positive terminal of the battery. In the series configuration there is only one path for the electrons to flow along.
If we place two lamps in a series circuit, they will both shine, but if one of the bulbs breaks, then the entire circuit stops working because there is only one path for the electrons to flow along. You might have seen this with strings of light such as fairy lights. When one bulb pops, the whole string of light stops working.
A solution to this is to wire the lamps in parallel. When we do this, we provide the electrons multiple paths. If one lamp stops working, the circuit will continue to work except for the one broken path. Let's look at voltage first in parallel circuits. Say we take a 1.5V battery.
If we use a multimeter to measure across the two ends, we will read 1.5V. But if we measure the same end we get a reading of zero. Why? Because we can only measure the difference in voltage between two different points. Voltage is like pressure in a water pipe.
If you fill up the tank then the water pressure is high, and we can read the pressure with the pressure gauge. The gauge is comparing two points in order to know what the difference in pressure is. This will be the pressure inside the pipe compared to the pressure outside the pipe. When the tank is empty there is no pressure difference because the pressure inside the pipe is now equal to the pressure outside the pipe.
So therefore we get a reading of zero. The same with voltage. We can only measure the difference in voltage between two different points. When we connect a component to a battery it experiences the difference in voltage between the two points or terminals of the battery. The voltage or pressure will force electrons to flow through the component.
In parallel circuits the voltage is the same anywhere in the circuit. It doesn't matter if we connect our multimeter here, here or here. We get the same reading. Why?
Because each component or path is connected directly to both the positive and the negative terminals of the battery, so they receive the full pressure. In series circuits the components were connected to each other, so the voltage reduced. But with parallel there are multiple routes and each is connected directly to the battery.
So when we use voltage in the formulas for parallel circuits, it's super easy because it's the same value. It's just the voltage of the connected battery. For example, in this circuit the total current is 2 amps and the total resistance is 3 ohms.
So what is the voltage of the battery? Well, from Ohm's law we know that we need the formula voltage equals current multiplied by resistance. So voltage equals 2 amps multiplied by 3 ohms, which gives us 6 volts.
Another example. This circuit is connected to a 12-volt battery. What is the voltage drop across the end lamp?
Well, that's easy. We calculate voltage again by multiplying the current and the resistance. It has a current of 1.5 amps flowing through it and a resistance of 8 ohms. 1.5 amps multiplied by 8 ohms gives us 12 volts. If we connected two 1.5-volt batteries in series, the voltage increases to 3 volts.
Why? because the electrons are being boosted by the second battery, so they increase in pressure or voltage. However, when we connect batteries in parallel, the voltage doesn't increase.
We only get 1.5 volts. Why? Because the batteries can't boost each other in this configuration. The path of the electrons is joined and then it splits, so the flow of electrons are shared between the batteries.
The batteries therefore can't provide more voltage. However, their storage capacity has increased. so they can provide 1.5 volts for longer than a single 1.5 battery by itself.
We've covered the basics of voltage in detail in our previous videos. Do check that out, links down below. So how does current flow in parallel circuits?
Remember current is the flow of electrons. We need electrons to flow in the same direction to power things like lamps. We apply a voltage difference across a component to force electrons to move.
As we apply more voltage, more electrons will flow. The speed of the electrons remains the same, but the amount of electrons moving will vary. The more electrons we have moving, the higher the current.
We represent current with the capital letter I, and we measure current in a unit of amperes, but we'll usually just shorten this to say amps. If we connect a lamp with a resistance of 1 ohm to a battery rated at 1.5 volts, the total current in the circuit will be 1.5 amps. We can measure that by placing a multimeter into the circuit. Or we can calculate that using Ohm's law and the formula current equals voltage divided by resistance. We won't go into too much detail on Ohm's law as we've covered that in a separate dedicated video.
Do check that out, links down below. If we then connect a second 1 ohm resistive lamp into the circuit wired in parallel, the multimeter reading the total current sees an increase to 3 amps. But if we measure the current through the lamps individually, we see the multimeter will read just 1.5 amps on each. In the wire between the two lamps, we also see a current of 1.5 amps.
We can see that the current will divide and the electrons will flow in all the different routes available to get back to the battery, and then they will recombine. We can also see that the total current is the sum of the current in each branch. So we calculate the total current using the following formula.
If we replace lamp 1 with a 2 ohm resistive lamp, so that's now double the resistance on that branch, then the total current decreases to 2.25 amps. Lamp 1 sees a current of 0.75 amps and will be less bright. Lamp 2 continues to read 1.5 amps.
and the meter between lamp 1 and 2 continues to see 1.5 amps. Therefore we can see that the current flowing in the branch depends on the resistance of the branch and again the total current in the circuit is the sum of the currents in each branch. If we add a third 1 ohm lamp into the circuit and we change lamp 1 back to a 1 ohm resistive lamp also, so that's now three 1 ohm lamps in parallel, we see that the total current in the circuit is now 4.5 amps.
Each lamp continues to see just 1.5 amps of current. The multimeter on the wire between lamps 1 and 2 has increased to 3 amps, but the meter between lamps 2 and 3 reads just 1.5 amps. If we double the voltage from 1.5 volts to 3 volts, then the current will double also.
The total current increases to 9 amps, the current between lamps 1 and 2 increases to 6 amps, and each lamp now experiences 3 amps of current. So from this we can see that the voltage applied will vary the current. The total current also varies with the resistance of each branch and how many branches are connected.
Let's see some more detailed explanations on how to calculate this. See if you can solve this before I do. Take this simple parallel circuit with two resistors and a 12 volt battery. Resistor 1 is 15 ohms and has a current of 0.8 amps.
Resistor 2 is 24 ohms and has a current of 0.5 amps. So what will the multimeter read for the total current in the circuit? Well we know that the total current in the circuit is equal to the sum of the currents in all the branches. Therefore 0.8 amps plus 0.5 amps is 1.2 amps.
What if we know the total current and the current in one branch? How do we find the current in the other branch? Well that's easy, we just subtract.
So in this example we have a 12 volt battery connected to two resistors. The total current is 3 amps. and branch 1 has a current of 1.8 amps.
The current in branch 2 is therefore 3 amps subtract 1.8 which gives us 1.2 amps. How do we calculate the current in a simple branch? We use the formula current equals voltage divided by resistance. Let's say we have three resistors wired in parallel to a 6 volt battery. Resistor 1 is 10 ohms, resistor 2 is 2 ohms, and resistor 3 is 5 ohms.
What's the current flowing through each? Well let's look at resistor 1 first. Current equals voltage divided by resistance.
So 6 volts divided by 10 ohms gives us 0.6 amps. Resistor 2 is 6 volts divided by 2 ohms which is 3 amps. And resistor 3 is 6 volts divided by 5 ohms which is 1.2 amps.
So the current in this part will be 1.2 amps because there's only the current from the single resistor. The current in this wire will be 4.2 amps. because there's the current of resistor 2 and 3 passing through it.
The current here is the total current which is 4.8 because of the current in all three branches flowing through it. Okay, so how do we calculate the total resistance in a parallel circuit? This is the part which people struggle with the most. It looks difficult because of this formula, but it's actually very easy and I'm going to show you how. And to make it even easier we've built a free online calculator for you.
and this will help you find the total resistance in your parallel circuit. You can find links to this in the video description down below. In the series circuit the total resistance of the circuit was the resistance of each component just added together. Why? Because the electrons had to pass through each one.
So the more resistors they pass through, the more total resistance increased. But with parallel circuits we're providing lots of different paths for electrons to flow through. So we're instead going to work out how conductive each branch is, or how easily electricity can pass through each branch. We then combine these values and we convert that back into a resistance. Let's take this simple parallel circuit with two 10 ohm resistors.
How do we find the total resistance of the circuit? Well we have to use that formula which is RT or resistance total equals 1 divided by 1 divided by R1 plus 1 divided by R2. So we then replace the R1 and the R2 values with our resistor 1 and our resistor 2 values. So we start at the bottom and we divide 1 by our 10 ohms for both which gives us 0.1 plus 0.1.
So we add the two decimals together to get 0.2. So then we just divide 1 by 0.2 to get 5 ohms of total resistance. If you do this in your calculator or in Excel then just remember to use your brackets.
So although we had two 10 ohm resistors, the total resistance is only 5 ohms. That's because the current has been split and so the resistance has reduced. If we had two 5 ohm resistors then the total resistance is 2.5 ohms. If we had a 10 and a 5 ohm resistor then the total resistance is 3.33 ohms. If we have more resistors then we just keep adding them into the formula.
We input our resistor values and we get again 3.33 ohms. For example a 10 ohm, a 5 ohm and a 2 ohm resistor gives us a 1.25 ohms total resistance. So why are we using all these 1 divided by resistor fractions in the formula? Well you don't really need to remember why we do it, you just need to remember how to use the formula.
But I'll just explain briefly why we do it this way. Because there are so many paths for the current to flow through, we instead work out how well electricity can pass through each path. That's the conductance, which is the opposite or the reciprocal of resistance.
As we already know the resistance value of the resistors, we can just invert this value to find the opposite. Looking at a 10 ohm resistor, we can also write 10 equals 10 divided by 1, because 10 divided by 1 is 10, and you can do that with any number. Then we invert the number.
to find the conductance of the reciprocal and we do that by flipping the denominator and the numerator. So we get 1 divided by 10 which is 0.1. We can flip it back to resistance by gain divided by 1 because it's the opposite.
So 1 divided by 0.1 is 10. If we had a 1 ohm resistor then we have a conductivity of 1. If we had a 1000 ohm resistor then we have a conductivity of 0.001. So you can see that it's going to be easier for the electricity to pass through the 1 ohm resistor because it has a better conductivity. So once we work out how conductive each path is, we add them together to find our total conductivity.
As we saw a moment ago, we can convert that back to resistance by taking the reciprocal. So one divided by the total conductance gives us our total resistance. Hopefully that made sense. If it didn't, then don't worry about it too much.
You're never going to really need that. You just need to use the formula. Power consumption in parallel circuits. The resistors and the components will convert the electrical energy into thermal energy as the electrons pass through and collide within the components. That's why they become hot and we can see that using a thermal imaging camera.
So how much power are the individual components and the circuit in total consuming? We can use two formulas for this. Either voltage squared divided by resistance or voltage multiplied by current. Let's see some examples.
Say we have a 10 ohm and a 5 ohm resistor connected in parallel to a 6 volt battery. R1 has a current of 0.6A. That's 6V divided by 10Ω which gives us our 0.6A. So the power consumption of the component is 3.6W. And 6V squared equals 36, so 36 divided by 10 is 3.6W.
Alternatively, 6V multiplied by 0.6A also gives us 3.6W. R2 is 5Ω with a current of 1.2A. That's 6V divided by 5Ω which equals 1.2A. So the power consumption is 7.2 watts. We see that from 6 volts squared divided by 5 ohms.
6 volts squared is 36, so 36 divided by 5 is 7.2 watts. Alternatively, 6 volts multiplied by 1.2 amps also gives us 7.2 watts. The total power consumption is therefore 3.6 watts plus 7.2 watts, which is 10.8 watts. We could have also found this by multiplying the voltage by the total current.
Or alternatively we could have used the voltage squared divided by the total resistance. Ok, now let's see if you can solve these problems. I'll leave a link in the video description for the answers and the solutions.
Question 1. We have four resistors in parallel. A 10 ohm, a 20 ohm, a 2 ohm and a 3 ohm. What is the total resistance of the circuit?
Question 2. We have three resistors connected in parallel to a 6 volt battery. The total current in the circuit is 2.5 amps. Resistor 1 is 10 ohms with a current of 0.6 amps. Resistor 2 is 15 ohms with an unknown current.
And resistor 3 has an unknown resistance value and an unknown current. calculate the current flowing in resistor 2 as well as the current and the resistance of the resistor 3. Okay guys, that's it for this video, but to continue learning then check out one of the videos on screen now and I'll catch you there for the next lesson. Don't forget to follow us on Facebook, Twitter, Instagram, LinkedIn and of course TheEngineeringMindset.com