Electrical Energy Part 2

Voltage  =  Current   x   Resistance 

V=IR

Voltage is the difference in charge between two sides of something

Current is the flow of Electrons - electrons have a negative charge

Current is measured in amps.  1 amp is 6 quintillion electrons moving past a point in 1 second. 

1 coloumb is 6 quintillion electrons. 

So 1 amp is 1 coulomb moving past a point in 1 second.

The symbol for current is I. I is measured in Amperes, or A. So I is A

I = A 

1 Amp = 6 quintillion electrons (1 coloumb) per second

Resistance is the oposition to the movement of current

Have a play with the Dude model part II - what happens to the movement of the electrons as you increase the temperature?

This is why it is important to cool your PC - if it gets hot it will slow down! 

If you want to make your PC go faster, get it colder. This is why liquid cooling is better, but more expensive, than air cooling

Resistors are any component in a circuit that will transform electrical energy into something else - light energy, heat energy, sound energy, kinetic energy (via magnetic energy)

Resisters have the unit ohm 

Resisters have the unit ohm, this is written with the symbol Ω   

Ω 

Resistors restrict how many electrons can flow through them for a certain potential difference. They do this through a variety of methods - for some they change the type of material they are made from - so metal to carbon then back to metal. For others, they simply get skinnier. A narrow wire cannot carry as many electrons through a point per second that a thick wire can for a given voltage

So, like in the cartoon below, the resistance restricts the flow of electrons for a given voltage. Increase the voltage and more Amps will flow for a fixed resistance. Increase the resistance and the amps will decrease for a fixed voltage

If we have a fixed resistor, then if we increase the voltage we will increase the current. 

We can see this mathematically. Lets say that Voltage is 6V and Current is 6A and resistance is 1 ohm

Then: 6V = 6A x 1 ohm

If we double the voltage, the current should also double

12V = 12A x 1 ohm

This is known as Ohms law

Voltage = Current x Resistance 

This is abbreviated as V=IR

V = IR

Now that we have the mathematical representation of the relationship between these variables - the formula, we can always find the 3rd if we have 2 variables

For instance

If we have 6V and 3A then what is resistance?

V=IR

6V = 3A x R

Rearrange to isolate R

V=IR

R = V/I

R = 6V / 3A

2Ω  = 6V / 3A

So then using these easy numbers (6, 3, 2) we should always be able to rearrange any 3 variable equations

To get Voltage: 6V = 3A x 2Ω V=IR

To get Current: 3A = 6V / 2Ω I=V/I

To get Resistance:   2Ω  = 6V / 3A    R=V/I 

Power - Energy per second - P=IV - Watt?

So when we looked at ohms law we saw that

V=IR

So if R is a constant 2 Ohms, and we start with a Voltage of 6V then current must be 3A as shown above

6V = 3A x 2Ω 

Lets say that this is what is being used to light a bulb and the voltage is being produced by hand crank

If resistance is fixed 2Ω  then if we double the Voltage to 12V what happens?

12V = 6A x 2Ω 

So we doubled the current. What you should also see is that the bulb gets brighter too

Also to double the voltage and current you had to put in more energy. If it was a held held crank, you would have had to spin it 4 times faster. Four times as many Joules of your energy to double the Voltage and double the Amps.

In other words, you got more light energy out, but you had to put in more kinetic energy spinning the generator

The energy is used to increase the voltage, this then moves the electrons. 

If you have a ruler and paper, you put energy in rubbing the ruler on your hair - the longer you do this, the more energy you have put in, the greater the voltage

If you put energy into recharging your phone to 100% and then turn it off, it will stay at 100% for a long time. If you turn it on and play YouTube shorts for the next 5 hours, the electrons will move through the monitor and speaker, doing work turning electrical energy into light and sound energy. It then goes flat. Suppose you charge it till it is 50% full and do the same. In that case, you will only be able to play 2.5 hours of YouTube shorts - you put half the energy in to moving the electrons back to the charged side of the battery, so not as many of them got moved, so the difference in Charge, the voltage is not as great as it could be. So, when those electrons move again through the screen and transform that energy into light energy, they can only do so for half as long.

Lets say we take a bulb and hook it up to our powerpack

The wire in the bulb has a fixed resistance of 2Ω

We then set the powerpack up to 6V. We take a subjective opinion of the brightness of the bulb and say it is bright

We then crank up the powerpack to 12V. This time the bulb is WAY brighter

So what is going on?

We can use ohms law to work out the amps. 

V=IR

V/R = I

6V/2Ω = 3A

and 

12V/2Ω = 6A

So, we find that for a fixed resistance, doubling the Voltage doubles the Current. 

However, our bulb is not twice as bright, its like 4 times brighter. So what is going on?

Well, each 1 amp is now being pushed by more Voltage. And there are more Amps being pushed by more Voltage. So we multiply it

It was: 6V x 3A = 18 Joules per second

It is now: 12V x 6A = 72 Joules per second

We can write a formula for this

Voltage x current = Joules per second

How much Voltage is each Amp being pushed by TIMES how many Amps are being pushed = how much Energy it is using per second. 

VxI = J/s

What could we say instead of saying Joules per second?

Joules per second is what?

Joules per second is Watt


Watt = Joules per Second


Well the more Joules of Energy that a thing can Transform from one type of energy into another per second, the more powerful that thing is

My Laptop can transform 120 Joules of energy from electrical into light, heat and sound Energy.  - Say what? 120W

My Alienware PC can transform 850 Joules of energy from electrical into light, heat, sound and kinetic Energy (the cooling pumps and fans). Say what? 850W

So we would say that my PC is a lot  more powerful

My girlfriends car is a Suzuki Swift with a 70,000W engine, meaning it can turn 70,000 Joules of chemical potential energy in petrol into Kinetic energy 

My car has an engine that can turn 185,000 Joules of chemical potential energy in petrol into Kinetic energy - say what? It has a 185,000 Watt engine.

So my car is a lot more Powerful

Power is how much energy is being transformed per second. Its unit is either J/s or W.  Joules per second is a lot of letters, Watt is a bit tidier

Electrical Power is 

Power = Current x Voltage 

P = IV

Lets go back to our bulbs

6V x 3A = 18W

12V x 6A = 72W

The bulb is 4 times brighter because it is transforming 4 times as much Electrical energy into Light energy per second 

The higher the wattage, the more joules will be transformed per second from electrical energy into other types of energy. 

LED lights have lower wattages than traditional bulbs but are just as bright. Why?

Well that is because they are more energy efficient. LED bulbs transform more of their electrical energy into light energy. Where as Traditional bulbs transform more of it into heat energy. 


Power = Current x Voltage 

P = IV

Watt

Total Energy

Every wonder why you get in trouble when you leave the lights on in your house

It is not because your parents don't like you...... I think ... its is because you are constantly transforming energy

If my Alienware Aurora PC has a power of 850Watts, and I use it for 5 hours - how much total energy was transformed by it?

Well, 850 Watts means it transforms 850 Joules of energy every second that it is one - that energy came from a giant generator spinning in a hydroelectric dam - so it is falling water that powers my computer. 

Anyway, 850 Watts is it's maximum - it is usually transforming a lot less but lets say it is operating at max to mine bitcoin for 5 straight  hours

850 W (Joules per second) x 3600 seconds per hour x 5 hours = 15,300,000 Joules in total 

15MJ

Thats the same as the energy in half a litre of petrol. 

Also, the same as the energy in 600 grams of chocolate (wow chocolate has a lot of energy in it.)

Using an online calculator, like the one below, you can find out how much it will cost you. 

For my Bitcoin operation, it will cost $1.40 for those 5 hours - but times that by 365 days, and that is $500 dollars per year. 

The link below is a calculator for working out your electricity bill. Try it for your PC and see what it actually costs (NZ cost per KWh is $0.33)

https://www.rapidtables.com/calc/electric/electricity-calculator.html

Also, have a look at how total energy is calculated in this Energy Consumption calculator below:

https://www.rapidtables.com/calc/electric/energy-consumption-calculator.html

So to calculate Total energy you take the energy used per second, a times it by how many seconds you are transforming energy for. 

Total Energy = Energy per second x Time (seconds)

Total Energy (Joules)  = Power (Watts) x Time (second)

Total Energy (J)  = Power (W) x Time (s)

Δ E = Pt 

Circuits

One Bulb

 Simple Circuit

Electrons need a path to travel along

Here are two circuits - they both have a switch

In the first the switch is open - making a gap that the electrons cannot cross (unless there is a very high voltage, then they will 'arc' and jump across)

So, even though there is a 9V charge difference, they cannot cross and stay in disordered motion rather than in a current 

On the other side, you can see the switch is now 'closed' this turns the bulb 'on' this is because the electrons can now move in a single direction - this is the current.

As you can see on the Ammeter (a meter that measures amps) the current is 0.9Amps.

Remember that a Amp is 6 Quintrillion electrons past a point per second. 

There is a Voltage of 9Volts across the battery, showing the size of the charge difference across the battery. This is the same as across the bulb. The bulb has a resistance of 10 Ohms. This means that each Amp in the Current will all 9Volts of potential difference to get across that one bulb. THat energy used will be transformed into heat and light. We can calculate how much energy is being transformed per second by times'ing how many amps are going through the bulb per second by the Voltage being used in the bulb. This will  give us joules per second, which is what? Watts. Thus this is power

Current x Voltage = Power

0.9A  x  9V = 8.1W

It is the resistance in the bulb that dictates the current. If we didn't  have a bulb in the circuit, too many electrons will flow (as nothing is stopping them from all going fast) and the wire will get hot and start to melt. This fire hazard is prevented in circuits by putting in 'resistors' and 'fuses' - a resistor will control the current in the circuit to prevent damage to the components. A fuse will 'blow' if too much current enters a circuit - your house will have fuses - this prevents electrical fire in the walls of you house when you leave all the lights on, and your PC and your TV and your PS5Pro.... So when a fuse blows in your house - you must have too many things on at once, so turn them off before you have a fire. 

The bulb is controlling how many electrons can flow through. It is the Resistor, controlling  the flow of Amps for a given Voltage. 

Increase the voltage and more amps will flow.

Lets compare the two batteries: 9V and 18V. As you can see, the higher voltage will force more electrons, Amps, through the bulb even though its resistance if fixed. This increase in Voltage per Amp combined with the linear increase in Amps results in a significantly brighter bulb.

Lets do some that's on this, keeping the bulb with a fixed resistance of 10Ω. We can work out V=IR and P=IV

V/R = I

9V/10Ω =  0.9A

18V/10Ω = 1.8A

VI=P

9V x 0.9A = 8.1W

18V x 1.8A = 32.4W

So, by doubling the Voltage we double the Amps. This results in 4 times the Wattage! so the bulb is 4 times as bright!

32.4W / 8.1W = 4 


Two bulbs

 Series Circuit

If we put two bulbs into the circuit then they will still only have that 9V push/pull to get from one side of the battery to the other. Because there is now two bulbs, there are now two resistors. 

When there is only one bulb the voltage drop across the bulb was 9V

With two bulbs the voltage drop across each bulb is 4.5V. 

Its like a 9 meter staircase. You are walking down a high stair case, you can walk all they way from the top to the bottom in one go 9 meter drop

But if you put a landing in half way, you can only drop 4.5 meters. (for safety). 

So the total change in potential is still 9, but each individual drop is only 4.5

Same with the bulbs. The total voltage is 9Volts. But the difference across each bulb is 4.5Vollts

Notice that the bulbs are one after the other. Much like TV series where one episode follows another. Thus, this circuit is called a Series circuit. All of the electrons must follow each other in a series that has various components that resist their movement. Thus all the electrons must cross all of the resistors. 

In this series circuit you will see that the current has reduced. Why?

Well that is because there  is more resistance in the circuit in total. Each bulb is a resistor - with more bulbs you have more resistance. This resistance adds up

Total resistance = Resistor 1 + Resistor 2

Rt = R1 + R2

So, total resistance is:

10Ω + 10Ω = 20Ω

Thus, if we use V=IR we can calculate total current:

We will use total voltage (9V) and total resistance (20Ω)

V=IR

I = V/R

I = 9V/20Ω

I = 0.45A

If we look at the total power of the whole circuit it is

P=IV

IV = P

0.45A x 9V = 4.05W

This is exactly half the power output of the single bulb circuit (8.1W). Because resistance has doubled.

What about the power at each bulb - how does the brightness at each bulb change

Because the voltage is shared across each bulb, the total is 9V divided by the two bulbs that are sharing it and we get 4.5V per bulb. The current has to go through each bulb, and we have already calculated the current as 0.45A. You can also quickly calculate to prove this for each bulb as a bulb is now 4.5V with a fixed resistance of 10Ω so that would be 4.5V/10Ω = 0.45A. 

Lets calculate the power output of each bulb

4.05W total divided by 2 bulbs = 4.05W/2 = 2.025W

Or

P=IV

IV = P

0.45A x 4.5V = 2.025W

 Parallel Circuit

What if we change it so that the two bulbs are not one after the other, rather one or the other

This makes two parallel paths for the elctrons to travel down

Each path has just one bulb

So each path has only 10Ω  of resistance

The electrons split at the junction. Those that go down the split off at the first junction will only encounter one bulb then return to the battery

Those that carry on past the first junction will go to the other bulb, that is the only bulb they will encounter then they will also return

Half of all the electrons will go down the first path to the first bulb

Half of all the electrons will go down the second path to the second bulb

Notic that these bulbs are each as bright as the single bulb circuit. Why?

Well, first we need to calculate the current for the first bulb using V=IR

V=IR, I = V/R

9V/10Ω = 0.9A

And for the second bulb

V=IR, I = V/R

9V/10Ω = 0.9A

Now lets calculate power for each bulb using P=IV

Bulb 1

9V x 0.9A = 8.1W

Bulb 2

9V x 0.9A = 8.1W

So each bulb has the same power as the single bulb circuit

In parallel circuits the voltage is the same down each path, the current is split

Well the current looks the same as the original 1 bulb circuit, but look at the current leaving and returning to the battery. It is the sum of the individual currents

0.9A + 0.9A = 1.8A

Thus the power of the whole circuit is

IV = P

1.8A x 9V = 16.2W 

If the battery is transforming 16.2 joules of energy per second, in this parallel set up, then the battery will go flat faster with the parallel circuit than it will in the series circuit. 

Notice also, that large returning current. As we keep adding bulbs, they all stay the same 9V/10Ω = 0.9A but the returning current keeps increasing


Now if we add more 10Ω batteries in parallel, they continue to follow the pattern of 9V, 10Ω, 0.9A. 

Notice that the current to the battery always sums to the current in each of the parallel branches.  

When we have 10 bulbs, the current across each path is still 0.9A, they continue to follow the pattern of 9V, 10Ω, 0.9A per path. 

But because there are now 10 paths, the current going into and out of the battery is the sum of 10 x 0.9A = 9Amps

If we double the Voltage to 18V, then the current will also double 

The current across each path is now 1.8A. And with 10 paths, the total current is 1.8A x 10 = 18A

Notice that the bulbs are brighter. This is because by doubling the voltage across each bulb, we have quadrupled the energy transformed at each bulb. What that is is the joules of electrical energy transformed into heat and light energy at each bulb in each second. Watt

It was:

P=IV

VI=P

9V x 0.9A = 8.1W

It is now

18V x 1.8A = 32.4W

So four times as bright

The total power for the circuit

It was 

8.1W x 10 bulbs = 81W 

or VI=P

9Vx9A = 81W

Now with double the voltage, it is

VI=P

18V x 18A = 324W

So by doubling the voltage, the total power of the circuit has quadrupled

You might also notice something interesting in the screenshot

The battery is on fire

High voltage will not cause a fire - but high Current will. The current is high enough in this example to melt the wires connected to the battery and start a fire


This is why there is a limit  to how many multiadaptors you can plug in to a circuit - too many and they will fuse OR catch on fire. 

You should always buy a multiadaptor that has a fuse

Modern fuses are just a bar of metal that bends as it gets hotter, as it bends it disconnects the circuit and breaks the circuit - It'll cool back down quickly - this allows you to unplug a few devices then continue using the multiadaptor - cheap multiadaptors do not have this - so pay more and save your house from a fire (fuses in multiadaptors are not a legal requirement - hence the 52 house fires in NZ caused by multiadaptors)

In the oldern days and in old houses, the fuse was a piece of wire - I used to have this type in my house

The video below is a demonstration of how they worked

Make your own Circuits

Have a play with the phet simulation below. Make a few different circuits, compare bulb brightness in a simple circuit, series and parallel. 

Put different components in a see what happens. 

The important ideas for Electricity are:

Voltage

I = Current

Power (Energy per second)

Energy (total)

Resistance

And 

Circuit types

Formula that you need to know:

V=IR          V = P/I

I=V/R        I = P/V

P=IV

ΔE=Pt 

R=V/I 

1 Joule per second = 1 Volt x 1 Amp 

VIPER

For any given circuit and for any component in the circuit you should be able to work out the following:

Voltage

Current (I)

Power (energy per second)

Energy (total)

Resistance 

This requires the following 3 equations

V=IR P=IV ΔE=Pt

These can be used as follows to answer VIPER

Voltage: V=IR or V = P/I

Current (I): I=V/R or I = P/V

Power: P=IV

Energy (total):  ΔE=Pt 

Resistance: R=V/I 

I explain how to use each in these two cringy videos titled VIPER 1 and VIPER 1 

Past paper Questions and Answers

@0 questions specially selected from 20 years of exam papers (2004 till 2024 derived).

Have a go at answering each question before looking at the answer. Do the questions in any sequence that you like

Remember VIPER and Remember your Units: V, A, W, J, Ω, s.

Electricity Past Paper Questions