Voltage Dividers Lab

In this lab exercise, we were asked to determine the range of source voltages that would guarantee a bus voltage in the range of 5.75 ≤  V ≤ 6.25 given that one to three loads in parallel were to be used with resistances of 1kΩ. This lab would reinforce the concepts of Thevenin equivalents and the voltage divider rule.

Our first step was to perform some design calculations. We were asked to compute the maximum and minimum  equivalent resistances of the one to loads in parallel. A single load would produce a higher equivalent resistance, since multiple loads in parallel produces an equivalent resistance that is smaller than the smallest load in parallel. Thus, we easily determined that the maximum equivalent resistance must be 1kΩ for a single load and and that the minimum equivalent resistance must be 333.333 ohms for three loads in parallel. Since voltage in general is proportional to resistance, we determined that the maximum bus voltage must be associated with the maximum equivalent resistance and that the minimum bus voltage must be associated with the minimum equivalent resistance. Through a formula given by our instruction on the whiteboard in front of class, we were asked to set up a system of equations that would allow to compute the required values of the of the source voltage and resistances. So Vs and Rs were found to have values of 6.53 V and 45.45 ohms, respectively. Through these values, we were able to compute the values of the maximum and minimum bus currents, which were found to be 17.25 mA and 6.25mA, respectively.

After these computations were established, we asked to take out the materials that we needed to perform the experiment. The loads were to be modeled using mounted resistors. A variable resistance box was to be used to model the source resistance. And finally, the voltage source used in this circuit was to be a bench top power supply. Short cables were to be used for the switches as open or short circuits.  Next, we were asked to place an ammeter in series with the source resistance and a voltmeter in parallel with the loads to measure current through and the voltage across the power supply. As usual, we were asked to measure each resistor with a multimeter and to compare their rated nominal resistances to their measured resistances. The nominal resistances, of course, were determined by their color codes.  As required, each resistor had a nominal value of 1kΩ. The measured resistances turned out to be 982 ohms, 978 ohms, and 988 ohms, which were all considered to be close enough values to 1kΩ. Next, we were to set the variable resistance box Rs as close 45.45 ohms as possible, since that was the value that we measured earlier. We calibrated it to 47.2 ohms. Likewise, we set the power supply voltage Vs, to 6.53 V, which again, was the value that we had measured earlier. It was calibrated exactly to a voltage of 6.53 V. The maximum bus current was found to be within the capability of the power supply. The maximum current was also found to be within the power capability of the resistor box.

The next step was to set up the breadboard. We were given a set of guidlines regarding how to set up the breadboard. We made sure that the power supply was de-energized until we were ready to perform the experiment.

We were now prepared to run the experiment. We had to collect the following data for the three loads: equivalent resistance (Req), bus voltage (Vbus), bus current (Ibus), and the calculated power delivered to the load. Load 1 had an equivalent resistance of 979 ohms, bus voltage of 5.49 volts, a bus current of 5.65mA, and a calculated power of 31.2 mW. Load 2 had an equivalent resistance of 489 ohms, a bus voltage of 4.75 V, a bus current of 9.80 mA, and a calculated power of 47.0 mW. Load 3 had an equivalent resistance of 326 ohms, a bus voltage of 4.25 V, a bus current of 13.19 mA, and a calculated power of 56.7 mW.

Now it was time to calculate to data and analysis questions. As mentioned in the previous paragraph, we had to compute the power delivered to each load, so please refer to the previous paragraph for that information. We computed voltage variations of 9.8%, -5.00%, and -15.0% for Loads 1, 2 , and 3, respectively. We predicted the adding a fourth load would cause a decrease in voltage variation. We also predicted that we would have to use smaller resistances and an increase in current in order to reduce the voltage variation.

The lab was now over and we were asked to disassemble the circuit. This was an interesting lab assignment and it provided us with another opportunity for us to get comfortable with creating circuits using a breadboard. It also helped us reinforced the concept of the voltage divider rule.

Introduction to Biasing

This laboratory assignment introduced us to the concept of biasing and also introduced us the structure and operation of a breadboard.  We were instructed to make the necessary change required for the given circuit to operate properly since the 9-volt battery exceeded the voltage rating of two LED lights (LED 1 and LED 2) connected in parallel with this power supply. Basically what we did was add some resistors (R1 and R2) in series with these LED lights in order to correct this problem.

Our first step was to model the circuit from a theoretical standpoint in order to compute the current, voltage, and power of each element. We were given that LED 1 and LED 2 had voltage and current ratings of 22.75mA/5V and 20mA/2V, respectively. From this information we used Ohm's Law to compute the resistance of each LED light, which were found to be 220 ohms and 100 ohms, respectively. Since resistor R1 was connected in series with the first LED, then by KCL, resistor R1 must have a value of 22.75 mA. Likewise, R2 must also have a current of 20 mA, since R2 was connected in series with LED 2. Next we used KVL to compute the voltage across resistors R1 and R2, which were found to be 4V and 7V, respectively. So these current and voltage values allowed us to compute the theoretical resistance values of R1 and R2, which were determined to have values of 178 ohms and 350 ohms, respectively. From here, we easily computed the power that should have been absorbed by R1 and R2 as 91.5 mW and 140 mW. It was also interesting that we were shown that resistor value are only made for certain discrete values. But since only five resistor types were available in the classroom, we determined that the closest values of R1 and R2 were 150 ohms and 470 ohms, respectively.

After when we done making the required computations, our next step was to take out the materials needed to perform the experiment. As with every other laboratory experiment, we had to use a multimeter to measure the resistance of each resistor separately in order to determine how accurate their resistance were in comparison with their rated values, which were determined by their color code. The nominal values in comparison with their measured values were 220/212 ohms and 470/464 ohms,  respectively. Since their nominal values were indeed close to their measured values, we deemed suitable for our experiment. Their power values were both deemed to be 1/8 W. We then took out our voltage supply and set it to 9 V, in order to simulate the 9 V battery. We were then given instructions regarding the structure and usage of breadboards and jumper wires. It was then time to perform the experiment.

In performing the experiment, we were instructed to set up three different configurations. Configuration 1 had us use both LED's, whereas Configurations 2 and 3 had use LED's 2 and 1 separately. We were then instructed to record the current through and the voltage across these two LED's. In Configuration 1, the measured current and voltage values for LED's 1 and 2 were found to be 12.8 mA/6.17 V and 14.7 mA/2.12 V, respectively. In Configuration 2, LED 1 had measured current and voltage values of 12.8 mA and 6.22 V, respectively.  Finally, in Configuration 3, LED 2 had measured current and voltage values of 13.2 mA and 2.12 V, respectively. Configurations 1, 2, and 3 had supply currents of 27.6 mA, 31.6 mA, and 56.2 mA, respectively.

The experiment was now over and we were told to disassemble the circuit and to answer the analysis questions. Given that the capacity of the 9V battery is 0.2 A-hr, we found that the circuit could operate for a maximum of 4.8 hours. We found that the percent error between the achieved LED current and the desired value with both LED's in the circuit was very high. The percent error for LED 1 was -43.7%, and the percent error for LED 2 was -26.5%. We determined that the percent errors were caused by the added resistors. As a result of these high percent errors, we ended up with a low circuit efficiency of 30.7%. Through theoretical computations, we noted that the circuit efficiency would rise if a 6 V battery were to be used. Although we recorded high percent errors and a low circuit efficiency, this lab helped us understand the concept of biasing and helped us practice to use the breadboard and how to cut jumper wires and to measure the resistance of these wires. Hopefully our next experiment will produce better results.

Transistor Switching Lab

The purpose of this lab was to introduce us to transistors and transistor circuits. As usual we began the lab by measuring the resistance of wires and to take out the breadboard. We were instructed to set up the circuit consisting of elements S1 (the pushbutton), R1 (180 ohms), R2 (10k ohms), R3 (680 ohms), Q1:2N3904, and a D1:LED according to a schematic diagram that was presented to us on our lab sheet. After doing so, we were instructed to press the push button and and to make an observation regarding the LED light.

As you can see, the light indeed turned on. We then used the voltmeter to check the voltages of the different elements in the circuit. 

The second part of the lab involved the fingertip switching. We were instructed to remove the push button and the R2 transistor and install two pieces of wire into the breadboard according to the diagram.  Then my lab partner placed both of the wires on his fingertip and noticed that the LED light glowed. 

After being instructed to lick his finger, my partner repeated this step again and noticed that the LED glowed even brighter. Next, we were instructed to measure the current flowing through a point A2 connected to the emitter given values of A1 connected to the base and to jot down these measurements in a table. The given currents through A1 were 0, 0.15, 0.30, 0.45, 0.60, and 0.75 mA, and we recorded values of 0, 38.02, 47.20, 52.30, 54.50, 55.10 mA, respectively for A2. This indicated a proportional relationship. Our instructor gave us a formula for computing the beta value, which was a simple ratio of A2 to A1, which was found to be 253.47 mA. The transistor was found to be saturated at 52.3mA. 

In conclusion, this was a very interesting lab assignment and and hopefully it will allow me and the other students to digest the textbook material regarding transistors much more easily. 

Introduction To DC Circuits

In this lab, we created a simple DC circuit with a battery, AWG #30 cables. and a load resistor.  The cables themselves were modeled as resistors is series with the load. Besides creating a simple circuit, we wanted to get comfortable using the lab equipment since this was our first lab assignment. One of our purposes was to determine the maximum amount of resistance that the cable could carry while the load could still operate normally. We also wanted to determine the largest distance of cable that could be used which separated the battery from the load. Additionally, we wanted compute the efficiency and to estimate how long it would take to discharge the battery.  Our first step was rather straightforward in that we theoretically modeled the active and passive elements of the circuit and computed the fixed load resistance as 1kΩ.  Next we gathered the materials needed to conduct the experiment. Since we knew that the load would require a minimum potential of 11V we had to vary the resistance of the cables. By doing so, this would help us determine the maximum amount of resistance the cable could have while the load could still operate properly. We would then keep track of the current through and the voltage across the load by using an ammeter is series and a voltmeter in parallel. respectively.  Then we were instructed to measure the components used for the actual experiment using a multimeter. We used a resistor box rated at 1W and a power supply rated with a maximum voltage and current rated at 12 V and 2A, respectively. Using the color code for the load resistor it's nominal resistance was found to be 1kΩ±10Ω. Using the DMM, we found the actual resistance to be 0.977kΩ. We also jotted down the rated power of the resistor which was 1/8 W. We also found it to be within the required tolerance. Our next step was to set up the power supply as close to 12 V as possible by adjusting the knob. We recorded this value to be 12.33 V. Finally came the point where we performed the actual experiment. Noting that the initial variable resistance was to be zero, we were instructed to increase the resistance of the resistance box by increments of 10 Ω until we achieved the minimum load voltage of 11V. Once getting to this point, we recorded the voltage across the load to be 11.0 V, the current supplied from the battery to be 11.3 mA, and the final maximum resistance of the cable to be 105 Ω.  The experiment was now completed and we were instructed to disassemble the components. We then got to the process of making data calculations. Considering that the power supply was rated as 0.8 A-hr, we determined time of discharge to be 70.8 hr. The next step was to compute the distribution efficiency. We did so by first computing the power to the load and cable to be 0.121 W and 13.4 mW, respectively. Given these values we noted that they did not exceed the power capability of the resistor box, which we noted earlier was rated at 1W. Then substituting these values into the efficiency equation, we determined the efficiency to be 90.0%. Finally, we were asked to determine the maximum length between the battery and the load, using the total resistance of the cable as a guide. We calculated this to be 304 m. We considered our lab to be a success, especially when you consider our relatively high efficiency of 90.0%. And we also met our other goals mentioned at the beginning of this post as well. Our first laboratory assignment was very enlightening, and hopefully it translates to success in our future lab assignments. The following are some photos that were taking during this lab assignment.