Experiment 10: Capacitor Charging/Discharging

Introduction: Capacitors are electrical components that store energy in the form of an electric field. This lab demonstrates the charging and discharging pattern of a capacitor.

- Calculate necessary circuit component values that will satisfy the objectives of the lab circuit.
- Create the circuit and run tests.
- Conclusion

Procedure:

First, we calculated expressions for a non-ideal charging/discharging capacitor circuit.

We then calculated for the component values of an ideal capacitor circuit such that the lab's parameters were met.

2.5 mJ of  Energy into the capacitor.

The variable resistance box has a max power output of 1W, which is more than enough for how we are using it.

Because the oscilloscope was set on continuous recording, we couldn't acquire the charging graph, so instead we used a stopwatch and a voltmeter to measure the voltage of the charging capacitor within 20 seconds.

Materials 1 Voltmeter and 1 stopwatch (optional), 1 oscilloscope, 2 variable resistors, 1 33 microfarad capacitor, cables.

The circuit setup, we found that the voltage of the charging time at around 20 seconds to be 11 volts.
The time taken for the capacitor to discharge took about two seconds which was expected.



Leakage Resistance:

Error calculation:

The charging and discharging graphs, how it should appear if the oscilloscope read once and not continuous.

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Conclusion: The experiment sucessfully proved the validity of the equations used for the charging and discharging of a capacitor. The leakage resistance was found to be roughly 10 times greater than the charging resistor, which is expected due to the leakage resistor being parallel to the capacitor.

Experiment 9 Integrating and Differentiating OP Amps

Introduction: We processed signals through a series of circuits with capacitors, resistors, and OP amps.

 

Integrating OP amp, Yellow = output Red = input voltage. Note the decrease in amplitude and similar frequencies.  

Saturation. The voltage applied to the OP amp wasn't enough to apply the necessary change, so the output became a square wave with a capacitor-like exponential decay.

Differentiating OP amp, not the increase in amplitude and similar frequency. The phase is noticeably shifted.

Experiment 8: Practical Signal Conditioning

Introduction:
     This experiment requires us to perform level-shifting and scaling processes of an operational amplifier to convert the temperature-proportional voltage in centigrade exiting out of the LM35 into voltage that is proportional to fahrenheit.

Procedure:
   We first start by testing the LM35, applying 9 volts into it relative to ground and seeing what voltage we get as output. Sure enough, we obtained 220 mA, or room temperature.

Now that the LM35 was shown to work, we solved for the output voltage of the op amp circuit according to this diagram.:

We also knew the formula for temperature conversion from celcius to fahrenheit, and we solved for the equation to be in terms of voltage.

Calculation:
Solving for the circuit diagram, we figured the output voltage to be related to the input voltage and the reference voltage by this relation below. Then we solved to find the reference voltage. We also took out resisters from the box that had the correct proportions to our calculated value.

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Pictures of the experiment:
Materials: 3 variable power supplies (9V, 9V, .4V) , lots of wires, breadboard, LM35 temperature sensor, OP amp, potentiometers...

The complete circuit.

power supplies

Output Voltage:

Error calculation. the .716 mA came from calculation from the value obtained through converting the output of the LM35 voltage into fahrenheit voltage using the celcius-temperature equation.

Conclusion

     The experiment successfully demonstrated the practical uses of an operational amplifier's ability to multiply and add. The conversion had an error of 9.2, which was probably due to the disproportion of the resistors to the actual ratio (18/22 isn't exactly .8) and the uncertainty of the resistors.