Thevenin Equivalent

Thevenin Equivalent

 

In this experiment we will be investigating a circuit that will be replaced with a Thevenin equivalent circuit. this is a picture of the circuit that will be replaced with  the Thevenin equivalent circuit.

 

 

 

 

 

 

 

we first proceed by calculating our Vthevenal. this was done by calculating our Vx which is the same as Vth. here is a picture of the calculation using nodal analysis. Vth= 8.64 volts

 

 

We also calculated our Rth= Rthevenal. here is a picture of the calculation. which was done by removing the voltage sources and closing the circuit. Rth= 65.94 ohms

 

 

now that we obtain our thevenin circuit, the experiment required a load when 8 volts were in such Rload. here is a calculation of how we obtained the Rload. this was done with Voltage divider Rule. Rload= 824.25 ohms 

 

 

once our calculations were done, we then proceed to build our circuit with the values calculated. here are some pictures of our assembled circuit.

 

 

 

 we also obtained the nominal and measured values of our circuit. here is a table of such measurements.

 

 

 

also the voltage in the Rload 2 = 7.91Volta and the theoretical was 8 Volts  which gave a percent error of 1.122 percent.

 

 

 

we dissembled our circuit and build the original one.

 

 

the voltage on the Rload 2 for this circuit was also 7.91 volts.

 

 

 

before dissembling our circuit we made sure that Vmax supplied to Rload 2 occurs when Rload = Rth. here is the calculation and several other calculations when Rload was different.

 

 

 

 

 

this experiment allow us to conclude that a circuit in fact can be replaced with a thevenin equivalent circuit. The values in this new circuit will be the same as in the original circuit. we also discover that the max voltage supplied to the Rload can be reached when our Rth= Rload.

 

 

 

 





Extra credit

Extra credit

 

 

NODAL ANALYSIS

 

 

In this experiment we will be modeling a real life circuit. this will be done by using several batteries as the power sources, several resistors as the cable resistors, and other resistors as the loads. The modeling of the circuit will look as follows.

here Is a drawn picture

 

 

here is a table that lists the components used, the nominal value, and the measured value

 

since on the circuit that we built we know two voltages, only the other two voltages will be unknown. In order to solve such unknown voltages nodal analysis technique was used in order to obtain the theoretical values, Here is a picture of the calculations

 

 

 

The theoretical values of the currents going out of the batteries were calculated. here is a picture of such calculation

 

 

 

After these calculations were done, we then proceeded to measure the values on the circuit built on the breadboard. here is a table of the theoretical and measured values.

 

 

 

 

 

here are the calculations of the theoretical and actual values of the power delivered by the batteries.

 

 

 

In this next part of the experiment our v2 and v3 are required to be at 9 volts. an now we will find our voltage supplied by the batteries. Here is the calculations

 

 

After finding the voltage that we needed the batteries at we then found the current of each batery

 here is the calculation of the power supplied by each battery (power supply)

 we then proceeded to change our power supply to our new voltage. here are the measurements that were found in our new circuit.

 

In conclusion, the purpose of this experiment was o analyze the power of using nodal analysis. Also to compare a circuit and the theoretical calculations with that to real life circuit. Even though our measured values were pretty close to the theoretical values, we can see that in real life there is many other variants that will make the values of the theoretical and actual differ.. 

 

 

 

 

 



TRANSISTOR SWITCHING

In this experiment we begin to discover how a transistor works. To begin we will begin by assembling a circuit like this.

 

 

 

 

 

 

after turning the led on, we then begin to remove the led and rebuild the circuit but this time with a potentiometer and two ammeters in order to measure the current of the base and the I of the emitter.

 

 

 

 

 

 

 

here is a table of our measurements, our measurements  are not exactly how the experiment required due to the range of our potentiometer. this small range of our potentiometer resulted in a deficiency of not being able to find saturation of the transistor.

 

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Milliamps passing through A1 Base current	Milliamps passing through A2
0.131	0.777
0.151	0.916
0.171	1.045
0.191	1.181
0.211	1.32
0.231	1.482
0.251	1.585
0.272	1.727
0.294	1.879

 Here is a graph of the measurements  with the rages that we could measure

 

 Here is a calculation of the Beta (gain) of the transistor. which is the slope of our graph shown above.

 

 

 

 

In conclusion we have found out that the transistor acts as a variable resistor and amplifier. the transistor acts as a variable resistor because as you add current trough the base there is less resistance and therefore the current through the emitter increases. the transistor also acts a an amplifier because even when putting our finger in the circuit, the led still had enough current to be turned on.

 

 

 

 

 

 

 

 



INTRODUCTION TO BIASING

 

we will develop a circuit with 2 led lights where different voltages and currents are required. In order to obtain the  voltages and currents are required we will add resistors to our circuit.

 

 

 

 

 

this is the calculation of the resistors  R1 and R2  that will be needed. also we will use physical resistors that are closest to our calculated resistors R1 and R2 

 

 

 

 

After the calculations we then proceeded to building our circuit. This circuit was built with two different led lights and two different resistors

 

 

 

 

 

Once our circuit was build we than proceed to adding a voltmeter and an amp meter to each branch where the current is divided. Here is a picture of the diagram drawn in the lab manual and the physical circuit. Note we only had two DMM, therefore we measured each branch once at a time.

 

 

 

 

 

 

 

 

After we had the measurements of the current and voltage drop, we than did the same measurements of one of the branches by removing an led. we also measured the other branch by removing the other led.

 

 

 

 

 

 

here is a table of the measurements

 

 

conf	Iled1	Vled1	Iled2	Vled2	Isupply
1	11.85 mA	4.7	7.71mA	1.99	19.37
2	14.93mA	5.72	X	X	14.93
3	X	X	12.06mA	2.06	12.06

 

 

Here are the questions and the solution of the questions asked in the lab

 

 

 

 

In conclusion the measurement were close to our theoretical values. the reason of why the discrepancy was due to the fact that we used different Resistors. The power out was only 40 percent of that of the power supply, this is possible because the other 60 percent was used in the resistors itself. We also concluded that the measurements obtained when the led's were removed were consistent with what we were suppose to obtain.

 

 

 

 

 

 

 

INTRODUCTION TO  DC CIRCUITS

 

first we emulated the battery, the cables, and the load with lab equipment

 

Battery= bench power box

cables= resistance box

load= resistance

 

 

this is the process to obtain the value of  R-load

 

the measured value is 989 ohms

 

the measured resistance of the box which will act as the R cable is 100.8 ohms

the measured value for V-load is 10.99 V

the current in the circuit provided by the power supply is 11.14 mA

 

 

 

Here is the calculation for the time of discharge

also the calculation of the power efficiency

power lost (power of the cable) 

 power out(power of the load)

 

 

 

 

 

 

 

 

Calculation for power efficiency

calculation for max distance of the cable

 

 

max distance is 298.08/2= 146.04meters

the value obtained has to be divided by two because there is two cables connected.

 

 

In conclusion the experiment is a good modeling for the real situation. with this experiment we get a sense of the power that is being distributed (power lost, power out).We also get a sense of how long our cable has to be.