Tips.
- As you know from previous lab, the capacitances are given with 20% tolerance (accuracy). This means that the capacitance value written on the capacitor (stated value) gives you only a ballpark idea what the capacitance is. You should not rely on this value in your calculations and use (more) accurate values for the capacitance you measured in the previous lab.
- You may notice that voltage measured by iOLab device fluctuates a little. These fluctuations are very small. When measuring voltages across circuit elements you may record voltage signal for the period of few seconds and take an average over this time interval.
Experiment 1. Resistors in series.
- Build the basic series circuit shown in the diagram (Figure E.1) – two resistors in series. Take
and 
. You may use other resistances for this experiment. The voltage 
across 
is registered by A7 terminal. A8 terminal will always show the voltage of the source, i.e. 3.3V. We only need A8 to verify the source voltage (it may get lower than 3.3V if the batteries in your iOLab device are low). The voltage 
across 
is the difference between A8 and A7 readings. - Use resistance values for
and 
and the voltage across the combination (3.3V) to calculate the equivalent resistance of the combination, current 
, and the voltages across each resistor. Your report should contain your calculations and comparison with the measured values of 
and 
. - Since the current through resistors in series is the same:
. Therefore
(E.1)
Calculate the ratios of the resistances and measured voltages
and
. Verify that the above relation is observed.
Show your values for
and 
in your report.
Experiment 2. Measuring unknown resistance.
In this experiment we will measure unknown resistance by connecting it in series with known resistance. You will be given unlabeled resistor. Your goal is to find its resistance 
.
- Build the basic series circuit shown in the diagram (Figure E.2) – two resistors in series. Take
or 
. The voltage 
across 
is registered by A7 terminal. The voltage 
across 
is the difference between A8 and A7 readings. Please note that 
and 
do not have to be connected in the order shown in the diagram. You just need to make sure you record appropriate voltages across them. - Use the proportion relation (E.1) from the previous Experiment to calculate unknown resistance
. - Your report should contain your measured values for
, 
, and your calculation for 
. - Please note that the technique used in this Experiment to measure unknown resistance will be used in many Experiments throughout this lab since iOLab device cannot measure resistance (and current) directly.
Experiment 3. Resistors in parallel.
In this experiment we will measure and calculate equivalent resistance for resistors in parallel. We will verify that the current thought equivalent resistance is the sum of currents through each resistor.
- Build the circuit shown in the diagram (Figure E.3). Take
, 
, 
, and 
. The voltage 
across combination of 
, 
, and 
in parallel is registered by A7 terminal. The voltage 
across 
is the difference between A8 and A7 readings, i.e. 3.3V - 
. - Use your measured values for
, 
and 
and the proportion relation (E.1) from Experiment 1 to calculate the equivalent resistance 
of the parallel combination of 
, 
, and 
. - Use values of
, 
, and 
to calculate (I.10) their equivalent resistance 
. Your report should contain your calculation of 
and its comparison with the value calculated in 2). - Calculate currents through all resistances in the circuit. Your report should contain values for
, 
, 
, and 
. Show that 
=
.
Experiment 4. Measuring sheet resistance.
In your kit you have a strip of slightly conducting black paper (Figure E.4). This paper has points in a lattice each separated by 1 cm. The ends of the strip have electrodes drawn on the paper with (highly) conductive silver ink. Our goal is to measure resistance between two (highly conductive) electrodes and calculate the sheet resistance 
of the paper.
- Attach the strip to the cork board with aluminum pushpins through the conducting electrodes on its ends. Make sure the pushpins’ heads have good contact with the silver ink electrodes.
- Attach alligator clip wires to the aluminum pushpins. Use the technique we implemented in Experiment 2 to measure the resistance of the paper strip - build the basic series circuit shown in Figure E.2. Sample implementation of this circuit for this experiment is shown in Figure E.5. Take
and measure 
(i.e. the resistance of the paper strip between two parallel electrodes). - What is the width W of this paper strip? What is the length L of this paper strip between two electrodes? Use (I.4) and your values for W, L and measured resistance R to calculate sheet resistance
of this paper. - Your report should contain the measured resistance
of your paper strip and your calculation of the sheet resistance 
.
Experiment 5. Resistance between two circles.
- Fix the conducting paper with the provided pushpins to the cork board through the circles of silver conducting ink. Make sure the pushpins’ heads have good contact with the silver ink circles.
- Attach alligator clip wires to the aluminum pushpins. Use the technique we implemented in Experiment 2 to measure the resistance between two circles - build the basic series circuit shown in Figure E.2. Sample implementation of this circuit for this experiment is shown in Figure E.7. Take
and measure 
(i.e. the resistance between two circles). - Use Model 1 to calculate theoretical estimate for the resistance between two circles. Use sheet resistance
value you measured in Experiment 4 and appropriate values for 
and 
in (M.8). Compare your theoretical estimate with your experimental value. What is the relative difference between theoretical and experimental values 
? - Your report should contain your measured and theoretical values for the resistance between two circles, relative difference between these values and your reflection on the accuracy of Model 1.
Experiment 6. Resistance between two concentric circles.
- Fix the conducting paper with the provided pushpins to the cork board through the circles of silver conducting ink. Make sure the pushpins’ heads have good contact with the silver ink circles.
- Attach alligator clip wires to the aluminum pushpins. Use the technique we implemented in Experiment 2 to measure the resistance between two circles - build the basic series circuit shown in Figure E.2. Sample implementation of this circuit for this experiment is shown in Figure E.9. Take
and measure 
(i.e. the resistance between two concentric circles). - Use Model 2 to calculate theoretical estimate for the resistance between two concentric circles in this setup. Use sheet resistance
value you measured in Experiment 4 and appropriate values for the circles’ radii 
and 
. Compare your theoretical estimate with your experimental value. What is the relative difference between theoretical and experimental values 
? - Your report should contain your measured and theoretical values for the resistance between two concentric circles, relative difference between these values and your reflection on the accuracy of Model 2.
Experiment 7. Kirchhoff’s rules.
In this experiment we will build the circuit and analyze it with Kirchhoff’s rules.
- Build the circuit shown in the diagram (Figure E.10 ). Use AA battery ( 1.5V ) and 3.3V terminal of iOLab device. Please pay attention to the polarity of batteries.
- Measure the potential differences
(the reading of A8 terminal) and 
(the reading of A7 terminal). Calculate the current through 2.2kΩ resistor. - Use Kirchhoff’s rules to solve the circuit (i.e. find currents in every resistor). Include your solution into your report. Indicate current values and directions on the circuit diagram and include it into report. You may use the diagram on this page or draw your own. Does the calculated value for the current in 2.2kΩ resistor match the measured value?
- Use your solution to calculate potential differences
and 
. Compare with the measured values. - Assume you replace all the resistors in the circuit with ones with resistances 1000 times smaller (
, 
, 
, 
). Will the currents in the circuit increase exactly 1000 times? Do you expect exactly the same measured values for 
and 
? - Is the AA battery supplying energy to the circuit or is it storing it (charging)? At what rate?
- Perform energy analysis of the circuit: for each element calculate the rate of its energy consumption. Add it all up to demonstrate that energy is conserved.
- Your report should contain your calculations for the circuit currents (loop equations and their solution) and the diagram of the circuit with currents indicated. Do not forget units. Include your answers for parts 4, 5, 6, and energy analysis in 7.
Experiment 8.
In this experiment we will build RC circuit and analyze it for cases 
and 
.
- Build the circuit shown in the diagram (Figure E.11). Pay attention to the polarity of capacitor.
- Make sure that the capacitor is initially uncharged.
- Connect the source (i.e. 3.3V terminal of the iOLab device).
- Please note that in this setup
, therefore the A7 terminal reading provides potential at both points D and B (relative to the ground). Record the potential differences 
(the reading of A7 terminal), 
(the reading of A8 terminal) immediately after the voltage source was connected (switch is closed at 
), and long time after (when the voltages are all constant, 
). - For the limiting cases of
and 
draw equivalent diagrams (without capacitor) and solve the circuits. Based on your solution calculate 
and 
for 
and 
and compare with measured values. - Your report should contain your equivalent diagrams and your solutions for
and 
for 
and 
. Also include comparison with measured values.
Experiment 9. Resistance of tetrahedron.
resistor along each edge (see Figure E.12). - Use the technique we implemented in Experiment 2 to measure the resistance between two vertices of the tetrahedron - build the basic series circuit shown in Figure E.13. The unknown resistance
is the resistance between two vertices of the tetrahedron. Take 
and measure 
as in Experiment 2. Use alligator clips to connect tetrahedron to the circuit. Sample implementation of this circuit for this experiment is shown in Figure E.14. - Draw a 2D equivalent circuit for the resistance between two vertices of tetrahedron made from identical resistors. Use symmetry to simplify the circuit and express it as combination of resistors in series and parallel. Calculate equivalent resistance between two vertices of tetrahedron. Compare your calculated value for the resistance with your measured value for the edge resistance of
. Do they agree? - Your report should contain your equivalent diagram for the tetrahedron and your calculation of its equivalent resistance in terms of the edge resistance. Include the result of your measurement and your comparison between measured and calculated values for the tetrahedron with edge resistance of
.
Experiment 10. Power Dissipated by a Resistor.
- Use AA battery and provided 1Ω and 4.7Ω resistors to build the circuit shown in the diagram (Figure E.15).
- Ask TA to make an image of your circuit with thermal camera. TA will email you the thermal image and a regular photo of your circuit. Regular photo will help you to identify resistors on thermal image. Include both images in your report. Use images of your circuit to identify resistors that dissipate the most power. Your thermal image will look like sample thermal image in Figure E.16
- Calculate currents in each resistor and find power dissipated in each resistor.
- Compare results of your calculations with your observations. Your report should contain your circuit calculations of power dissipated in each resistor and comparison with thermal image observation. Also include thermal and regular images of your circuit.
- Repeat parts 1-4 for circuit shown in Figure E.17.
