BEE610 Maximum Power Transfer Theorem using Tinkercad and Circuit Safari

Today, we are going to see verification of maximum power transfer theorem.

So, for verification of the maximum power transfer theorem, I am taking this circuit, where RL is a load resistance, which we have to find what should be the value of the load resistance for maximum power transfer.

And if the load resistance is not equal to the resistance corresponding to maximum power transfer, what will happen.

So, for in order to calculate the maximum power transfer theorem, what we have to do?

We have to represent this entire circuit by its Thavenene equivalent.

So, this entire circuit up to this point, AB should be represented by Thavenene equivalent.

That means, this will be represented in this form, VTH is in series with RTH.

And we have seen that when the value of this RL is equal to RTH, when RL is equal to RTH, then power transfer to the load will be maximum.

Let us try to verify it.

So, first I want to calculate the value of VTH.

So, for calculation of the VTH, I am drawing the equivalent circuit.

For calculation of the VTH, the terminal A and B will be removed.

This is 10 volts plus minus.

So, these resistors are connected.

So, this is 10 volts, this is 10 volts, 5 volts, 10 volts and 5 ohms.

These are my terminals A and B. So, across these two terminals, I want to calculate VTH.

This is nothing but equal to VTH.

So, for finding this, because one reference point is also defined.

So, I am defining the nodes as the nodes A and B are defined here.

I am defining this as nodes C, I am defining this as node D.

I am going to apply the nodal analysis for finding this one.

So, let us try to apply the nodal analysis at each node.

So, first I am applying at node D if you are applying the nodal analysis.

So, this will be equal to 10 minus VTH divided by 10.

10 minus VTH divided by 10, this indicates the current that is entering.

So, we will divide in two currents, let us assume they are leaving.

So, this current to leaving will be VD divided by 10, because that current passes through this 10

ohms plus VD minus VC divided by 5, that current passes through the 5 ohms resistance.

So, this when you simplify, you will get it as 4 times of VD minus 2 times of VCE is equal to 10.

Let us take it as equation number 1.

Similarly, applying this at node C, I am just applying the nodal analysis at node C.

So, now the current entering will be VD minus VCE divided by 5.

So, now this current whatever is entering, because this is open circuit, all the current will pass like this only.

So, this will be equal to VCE divided by 10.

And we know the current passing through this, this current passing through this one will be equal to zero,

because the reason is it is open circuit.

So, now this can be simplified if you simplify this, you will get it as 2 times of VD minus 3 times of VCE is equal to zero.

Let us take it as equation number 2.

So, now solving equation number 1 and equation number 2.

So, when you are solving the value of voltage at node C, VCE will come as 2.5 volts.

So, VCE will come as 2.5 volts.

So, whatever voltage is coming at C, if you are applying the KVL in this loop, KVL in the loop, I am starting from here.

So, from here to here, because when you whatever is the voltage of across 10 volts, that is nothing but equal to VCE.

And the voltage of across 5 ohms is zero and minus VTH is equal to zero.

Or otherwise, whatever is the voltage at C, same voltage will be at node A, because of voltage of across this 5 ohms is zero.

So, we can tell this as VTH.

So, we got the value of VTH.

So, let us now try to calculate the value of RTH.

So, to calculate the value of RTH, what do you have to do?

We have to do it plays the voltage by the internal impedance.

So, internal resistances is zero.

So, at a mining I am representing as it is.

So, this is 5 ohms, this is 5 ohms.

So, this is 10 ohms.

So, here also this is 10 ohms.

So, these are my nodes A and B.

So, when seen into the circuit from here, whatever the value that is coming, that value is nothing but RTH.

So, now calculate, you can see here this 10 ohms is in parallel with 10 ohms.

So, parallel combination of two will become 5 ohms.

So, 5 is in series with 5, it becomes 10.

Again, now 10 ohms is in parallel with 10, it becomes 5.

Again, 5 is in series with 5, so it becomes 10.

So, RTH will become equal to 10 ohms.

So, we got the value of RTH is equal to 10 ohms.

But practically when you want to find using the circuit, so generally what we will

do?

We will calculate the value of ISC.

So, VT h by ISC in this form also, we can calculate.

So, let us try to calculate that also, because that practice also will be done.

So, if you want to calculate the value of ISC, again same thing plus minus this value is

10.

So, this is 10 ohms, this is 10 ohms, 5 ohms, 10 ohms, 5 ohms.

This is my node A and this is my node B.

This I am taking this my reference.

So, ISC is when you short circuit these two terminals, how much current is passing?

This current is called as ISC.

So, this is node C and this is node D.

So, again same thing I want to calculate using the nodal analysis.

So, using the nodal analysis I can apply at node D.

At node D if you are applying it will be 10 minus VD divided by 10 is equal to VD divided by 10

plus VD minus VC divided by 5 or this I can simplify as 4 times of VD minus 2 times

of VC is equal to 10.

This is what we got.

So, now coming to applying the nodal analysis at node C.

When you are applying nodal analysis at node C, it is VD minus VC divided by 5 is equal

to 1 current is leaving through this 10 ohms.

So, this will be VC divided by 10.

Another current is passing through this 5 ohms.

That is nothing but equal to ISC.

This is VC divided by 5 or from this I can simplify this one.

This will be 5 times of VC minus 2 times of VD is equal to 0.

This will get.

So, now again same thing I am solving equation number 1 and equation number 2.

So, I need to calculate the value of VC.

So, the value of VC will be equal to 1.25 volts.

So, from this I can calculate my value of ISC.

ISC is nothing but VC divided by 5.

This is nothing but 1.25 divided by 5.

So, this will come as 0.25 ohms.

We got the value of ISC.

Once you get the value of ISC, I can calculate RTH is equal to VOC divided by ISC.

So, the value of VOC is 2.5.

The value of ISC we got as 0.25.

This will be equal to 10 ohms.

So, in this manner also, we can calculate.

So, now I can summarize that.

So, this can be represented in this form VTH.

This is VTH is 2.5 volts.

This is in series with RTH.

This is VTH.

And the value of RTH we got as 10 ohms.

Getting it.

So, this is connected to RL.

You across the terminals A and B.

So, let us see, when you are varying this value of the resistance,

how the power across your load is changing.

So, for that I have already tabulated.

So, I am directly going there.

So, that it will be easy to analyze.

So, I am pasting the same circuit here.

So, let us see, under different conditions, how the things will come.

So, when RL is equal to 0, I am taking RL is equal to,

let us take RL is in ohms.

RL is equal to 0 ohms.

That means, when RL is equal to 0,

what will be the value of the current that is passing.

Let us calculate the current.

So, we can tell that current I will be equal to VTH divided by RL.

So, using this formula, I will calculate the value of current.

So, you want to calculate the power drop or power that is supplied to the load.

We will be equal to I square multiplied by RL.

I square multiplied by RL.

Or otherwise, we can calculate in terms of the voltage also.

In terms of the voltage also.

So, what is this value of I?

I is nothing but VTH divided by RTH plus RL.

This will be multiplied by I multiplied by RL.

I multiplied by RL is nothing but voltage drop across the resistance.

This voltage drop across the resistance.

You have to multiply with VTH by RTH plus RL.

Using that also, you can calculate or multiply with the current.

So, this I can write in this form.

Voltage across your RL.

This will be multiplied by the current.

Voltage across the RL multiplied by current.

Using this also, I can calculate.

So, now coming to the efficiency.

Efficiency is nothing but output divided by input.

What is the output?

Output is I square multiplied by RL divided by.

What is the value of input?

The power that is supplied from the input.

This current supplied by this one is I.

The current supplied by this one is I.

So, when the current supplied by this one is I.

The power that is supplied will be voltage multiplied by current.

So, this is nothing but equal to VTH multiplied by I into VTH.

This will be multiplied with 100 to get in percentage.

So, here I and I will cancel.

This will become I into RL divided by VTH into 100.

Or simply this I can write as voltage across.

Because I multiplied by RL is nothing but voltage drop across the resistance.

So, this will be V RL divided by VTH into 100.

So, whenever you are calculating the circuit practically.

So, efficiency can be calculated by measuring the voltage across the load divided by.

The total voltage, total voltage that is equal to VTH.

VTH value is fixed. That is 2.5 volts multiplied by 100.

So, using that also, you can calculate.

So, this will directly give the value in percentage.

So, now I have taken the different cases.

Let us take for example, if I am taking 2 ohms.

The current will be equal to V is 2.5 divided by RTH's 10 plus RL is equal to 2.

That means it is 12.

So, when you calculate, you will get it as 208.33.

Similarly, if you are calculating PL using this formula, I square multiplied by RL.

This current square multiplied by RL that will give 86.8.

And efficiency using this formula.

So, if you using this formula, that means I into RL divided by VTH into 100.

If you calculate, you will get this as 16.67 percentage.

Similarly, as you are going on changing the value, you can see 2, 4, 6, 8, 10, 12.

Like I have taken different cases.

As you are moving downwards, you can see the PL is going on increasing.

0 86.8, 1 27.55, 1 46.48, 1 54.32.

And when RL is equal to RTH, you can see this has reached to 156.25.

So, after this you can see again, the value will goes on decreasing.

We can observe that efficiency will be maximum at this case, it will go on falling down.

Similarly, sorry, this is the power across your load rate.

So, now coming to the efficiency, you will observe that as load resistance is increasing,

the efficiency will go on increasing.

And when RL is equal to RTH, the efficiency is equal to 50 percentage.

So, in order to understand this properly, I have plotted the same thing curve also.

You can observe here the plot of when the RL is varied, how the power is varied.

So, you can see here the power is maximum when RL is equal to RTH is equal to 10ones.

If you are taking the efficiency, the efficiency will go on increasing as the value of RL is increasing.

And when RL is equal to 10, you can see under this condition, the efficiency is 50 percentage.

So, same thing we are going to prove it practically now.

So, let us first try to solve it using TinkerCat.

So, after that we will go for circuit safari.

So, for this I am going back to TinkerCat.

So, for the time going to the TinkerCat.com, after that you have to go to the circuits.

After going to the circuit, you have to click on create news circuit.

Once you click on the create news circuit, so the TinkerCat.com will load.

So, once it is loaded, you have to select all, then you need a breadboard for implementing this.

So, I am selecting the breadboard.

So, once you select the breadboard, so that breadboard I can keep here, drag and drop here.

So, let us assume I am placing the breadboard here.

So, along with the breadboard, now the next thing that is required is the voltage source.

So, I am just typing here, I have to type the voltage.

So, voltage when you type.

So, here you can see there is a power supply.

So, this power supply I am keeping.

This power supply that is required is 10 volts.

So, 10 volts power supply I have connected.

Then one multimeter is required.

I am using the multimeter.

So, this multimeter can be used as a voltmeter, a meter or a resistance meter.

For measuring the resistance, we will see them one by one.

So, then we need to place the resistors.

So, for placing the resistor, I am deleting all.

Resister will be available in the outside only.

First, I have to rotate it.

So, I am using this button for rotating.

So, the value of the first resistance is 10 volts.

So, I have selected 10 volts.

So, this is 10 volts resistance.

Place it somewhere here.

So, after the 10 volts, one more resistor is required.

So, the value of this resistance required is again 10 volts.

So, this value is 10 volts.

So, after that one more resistor is required.

The value of the resistances is 5 volts.

So, first I am rotating it.

So, then I am selecting this one as 5 volts.

So, then I have placed here.

So, after placing the 5 volts resistor, one more 10 more resistor is required.

So, that 10 more resistance I have connected here.

The value of this resistance is in volts and it will be 10 volts.

So, after that again one more resistance is required.

So, this resistance I am placing here.

So, the value of this resistance is again in ohms.

This will be 5 ohms.

So, after that these two resistance should be connected together.

Again, these two I am connecting to some points.

So, that we can measure it easily.

So, now, this negative terminal of this voltage source will be connected to this point.

And, coming to the positive terminal positive terminal will be connected to this resistance.

So, now I am adjusting this voltage source somewhere here.

Okay, positive one negative are now connected.

Now, coming to measuring the value of VTH.

So, further the positive terminal is connected here.

Negative terminal is connected here.

Okay, once these are connected, so I can run the simulation.

So, when you run the simulation you can see you are getting the value of voltage across your load thickness.

A and B is 2.5 volts.

So, same thing we got theoretically theoretically.

So, we got also got as value as 2.5 volts.

So, now I want to calculate the short circuit current.

For calculating the short circuit current, what I will do?

I will convert this to the emmeter mode.

Emmeter mode means it will short circuit.

So, I can calculate the short circuit current.

That is 250 milliamperes.

So, we got the same thing ISE is equal to 0.25 amperes.

So, we got it in the distance.

This is one way.

So, if you want to measure the value of VTH, what you have to do?

You have to make your supply voltage as zero.

Once you make the supply voltage as zero, the meaning is it is replaced by the internal

distance.

So, now measure the resistance mode on the simulation.

So, now you have taken your supply to zero volts.

Now, you have keeping this multimeter in the resistance mode and measure across these two terminals.

You can see you are getting the value of RTH as 10 moons.

So, in this way I can find the value of RTH.

So, I hope you understand how to find RTH, ISE and VTH.

So, now I have to connect the other resistor.

So, I am just deleting this connection.

So, later on we will connect them again as per the requirement.

And this voltage source value, I am changing it to 10 volts.

Now, I have to connect load resistance.

So, that load resistance now I have connected across these terminals.

Now, this load resistance we will take different value.

So, first I am taking it as zero ohms.

So, for each case, we want to measure the value of the voltage drop.

Or we can measure the value of the current that is passing.

Because anything is one and the same, current passing through it.

Because current we have tabulated.

So, if I verify whether the same value of the current is passing in this case or not.

So, first I am taking the zero.

So, for this, this red color is connected here.

So, now I have to connect this resistance through thisometer.

So, for that what I am doing, I am just moving this little bit.

So, then I am changing this connection also.

This connection now I have connected.

So, now, then negative terminal.

The negative terminal is connected to this resistance.

So, now I am running the simulation.

So, you can see here, when the value of RL is equal to zero, the current that is passing

is 250 milliamperes.

Similarly, I want to measure the voltage also.

So, for that what I am doing, I am keeping one more multimeter.

So, this multimeter, I am connecting this volt multimeter and voltage mode.

So, again same thing to measure the value of the voltage.

The positive terminal is connected here.

And the negative terminal is connected to the second side.

Okay.

So, now we can get the voltage as well as current.

Voltage is equal to zero.

So, now what I am doing, I am changing this resistance value to 2 ohms.

Let us see what will happen.

When it is connected to 2 ohms, it is measuring as a 208 milliamperes.

And the voltage is 4 17 millivolts.

So, from this I can calculate the efficiency that is 4 17 milly divided by 2.5 volts into 100.

That will give you a percentage.

So, similarly, I can change the value to other values.

So, I am changing this resistance value to 4 ohms.

You can check the value.

Similarly, when this value is changed to 6 ohms, you can measure what is happening.

Similarly, change it to 8 ohms.

So, similarly, change it to 10 ohms.

So, when you are changing to 10 ohms, it is coming as 1.25 volts.

So, similarly, now I am increasing to 12.

So, 12 ohms.

12 ohms.

So, then, similarly, I am changing it to 14.

You can please cross-check with the table.

So, similarly, I can change it to 16.

So, similarly, I am changing it to 18.

And then, I am changing this to some value.

Let us take for example, 20.

So, by varying the value of the RL, how the parameters are changing.

We can measure easily.

By measuring this voltage, we can calculate the efficiency.

For measuring the current, we can easily calculate the value of the load that is transferred to your load.

That is, power that is transferred to the load you will be equal to.

The current multiplied by the voltage, product of these two will give the power that is transmitted.

This voltage divided by 7 and equivalent voltage into 100 gives you our efficiency.

I hope that how to verify the maximum power transfer theorem using Tinkercut is clear to you.

Let us now see how to calculate this, verify this maximum power transfer theorem using the circuits of RL in your mobile.

So, once you go to the mobile, so first I need a voltage source.

So, further, I have connected a voltage source.

This voltage source I have double-clipped.

So, here I can change the value.

So, my value is 10.

So, I have taken it as a 10.

Once the 10 volts are kept, then the resistors are required.

I am placing different resistors.

The value of the resistance that is required is 10.

So, 10 volts is fixed.

So, then one more resistance is required.

That series resistance is 5 volts.

So, I am changing this to 5 volts.

Okay.

Once it is changing to 5 volts, one more resistance is required.

That resistance is placed.

The value of this resistance is also equal to 5 volts.

So, I have changed it to this value also to 5 volts.

So, this is done.

So, now some resistors are required in shunt.

For rotating, I am using the third button on the right hand side.

So, this is rotated.

So, the value of this resistance.

This is also equal to 10.

So, I have made it 10.

Then coming to the second resistance, again I have placed here.

I have rotated.

So, the value of this resistance also equal to 10.

So, I have made it 10 volts.

Okay.

Once the resistance is placed, the load resistance will connect later on.

So, one is ground is also required for the reference purpose.

So, I have connected one.

Ground also here.

So, once these are connected, I am making the connections.

You have to click on the rectangle block.

Click on the rectangle block of the second block.

Similarly, when I click on the rectangle block, you can see it is converted to circle.

Click on the rectangle block of next one.

Similarly, made the connections.

So, this resistor will be connected here.

This one is connected here.

Similarly, this is connected to this one.

This is connected to this one.

And ground is connected to this point.

So, now, to measure the value of what I have to do, I have to connect a voltmeter for measuring the VTH.

So, for measuring the VTH, I am taking a voltmeter.

This voltmeter, I am just rotating as per my requirement.

So, this voltmeter, what I have to do?

First, I have to select the scope range.

So, scope range, I am taking equal to my battery value.

Because maximum value that can reach is equal to 10.

So, this I can reach is 10.

After this instantaneous value, we will change to DC average value.

Getting it.

So, once this is done, I am making the connection of this voltmeter across these two terminals.

So, once the voltmeter is made, just turn it.

So, you can see the value is going on changing.

So, once it is stabilized, whatever value it shows, that indicates the value of VTH.

So, you can see it is going on changing.

Now, you can see the value has stopped changing.

I am pressing the pass button on the rewind button.

So, now it is stopped.

You can see here, it is showing 2.5 volts average value.

So, that means the voltage is 2.5 volts.

So, now I want to measure the value of ISC.

For measuring the value of ISC, what I have to do?

I have to connect one meter.

The term meter also I am rotating as per my requirement.

So, now this term meter also I have to select the current range.

So, what can be the value of the current that can go?

So, let us take the value a little more.

So, I am selecting some value 4.

Then instantaneous value, I am taking as DC average value.

So, now I make the connections.

Okay, then again turn it.

So, now we can see the current value is changing.

So, once it is stabilized, we will measure the value of ISC.

So, once ISC comes, VTH by ISC, that gives the value of RTH.

That in that way, we can measure the value of RTH using the software.

Okay, 250 milliampere scale. You can see its top changing.

So, we got the value of ISC. So, VTH by ISC gives the value of RTH.

So, RTH will be equal to 10, because we got the value of VTH is 2.5.

Now, the value of ISC came as 250 milli. So, if you divide it, RTH came as 10 volts.

So, let us now see, under different value of the load resistance,

how the current passing through on voltage across is changing.

So, for that what I am doing, I am just deleting which other things are not required for me.

Okay, this one I am just rotating.

Okay, so now I want to place one resistor.

So, I am placing one resistor here. I am just rotating it.

The value of this resistance will go on changing.

So, now one voltmeter also I am taking for measuring the voltage.

It will measure the voltage across this resistance.

Okay, once these are done I am making the connections.

Okay, this voltmeter also I have to select this scope range.

So, scope range I am taking equal to my supply voltage only.

This is equal to 10.

So, now this instantaneous value should change to DC average value.

So, once changed I am making the connections.

Okay, now we can see all the commmeter voltmeter everything is connected.

So, let us see different values of the resistance, how this will change.

So, first I am taking the value of this resistance as zero.

When you select it as zero and run it.

So, now we can see that value is going on changing.

To 250 milliamputes game.

So, similarly if you want to change the other values again same thing.

So, here I am not checking for every value of resistance.

It will take so much time for changing.

So, I am checking mainly for some main main values.

So, I am checking for six modes for example.

So, you can verify for the six modes whether same thing is coming on.

So, you can trace cross check with the table that is plotted.

So, what is the value that is coming there.

You can see now the value stopped.

So, you can note down this value.

This is what the case of six modes.

Similarly, let us try to check it for 10 modes.

So, I am taking it as 10.

Okay.

So, now I am running.

So, you can see it stopped changing.

So, we got the same value as the theoretical value.

125 milliamputes and 1.25 volts voltage drop across the resistance.

So, now again similar way.

We can change it.

For changing, you have to press the rewind button.

Otherwise even if you change, that value will not change.

So, now 10 I am changing to some 14.

Let us take for example, done.

So, now I am again running.

So, for 14, we got the theoretical value as 104.17 milli.

So, let us see whether it is coming or not.

So, 104.1 milliamputes came here.

So, 104.17.

It is rounded up to 104.2 here.

Okay, you got that value also.

So, similarly, I am changing it to some 18,

18 ohms directly.

So, 18 ohms, we got the theoretical value as 89.285 milli.

So, let us see what will come practically.

So, we can see here it is top of the changing.

So, here also that value came as 89.29.

So, we got theoretical as 89.285.

It is nothing but 89.29 only.

So, hence we proved that whatever the theoretical value we got.

Same value we got practically also.

So, that value came as 89.29.

So, we got theoretical as 89.285.

It is nothing but 89.29 only.

So, hence we proved that whatever the theoretical value we got.

Same value we got practically also.

So, maximum power transfer theorem is verified.

Both using the 10 kar cards circuits are far as well as theoretically.

So, I hope that everything is clear to you.

If you still have any queries, you can leave your comments in the comment section below.

I will answer to your queries from there. Thank you.

Thank you very much.