Lab 17 RC circuit capacitors -> Capacitors in both Series and Parallel, Charge Buildup and Discharge in Capacitor, dual capacitor dilemna and error analysis, RC system data deriving equations, UNDERSTANDING OF UNITS<=

Capacitors in both Series and Parallel

 From this lab, we were given two capacitors that were 1 uF each. The value actual value for each capacitor was found and recorded to be 0.965 μF and 0.978 μF. The capacitors were then put into a parallel circuit (as seen in the photo to the left. The capacitance was measured to be 1.979 μF. Then, capacitors were set up in series(as seen in the picture above) and the capacitance was measured to be 0.487 μF. From these values we can find a relationship between capacitors in series and in parallel. The relationship of total capacitance of capacitors in series is 1/Ctotal=1/C1+1/C2. In series, the charge is the same for the capacitors and so when looking at V=Q/C, the charge can be ignored and the only variable left is 1C. The relationship in parallel is Ctotal=C1+C2. In a parallel circuit, the voltage is the same for the capacitors and so when looking at the equation Q=CV, voltage can then be ignored and one can say C and V are proportionally related. From chart below, one can easily see how each of V, I, R variables can be calculated.

Solving the lab questions

Lab activities

General setup for Capacitor that charges rapidly and discharges rapidly

For this lab, a capacitor was charged up to show how energy is used up from it. As seen in the video below, first the light bulb is charged by the voltage. As the light dims and eventually goes out, that voltage charges up the capacitor. The two wires connected to the voltage box are then removed and put together (to close the circuit) and the light bulb turns on and once again, dims and eventually turns off. When the wires are removed from the voltage box and the circuit is closed, now the bulb is being powered by the capacitor. This lab showed how the capacitor works, its charged up and stores that power and then it is used up by other things such as the light bulb.

Charge Buildup and Discharge in Capacitor
Setup processes charging capacitor with dc source.

The capacitor was charged up to show how energy is used up from it. As seen in the video down below, light bulb is first charged by the voltage and as the light dims and goes out in around 5 seconds(not shown in video), that voltage is then charging up the capacitor. The two wires connected to the voltage box are then removed and put together (closing the circuit)  then, light bulb turns on and once again, dims and turns off slowly. When the wires are removed from the voltage source box, the circuit is closed, now the bulb is being powered by the capacitor. This lab showed how capacitor works; when it is charged up and stores energy and then used it up by resistor type of applications such as the light bulb. 

In order for the charges to be equilibrium, one had to calculate their relationship with each other. Because these capacitors are in parallel, the capacitance adds up and new capacitance of 0.94. The voltage can be calculated by Q/C and resulting 3.69 volts.

Percent error is -> (3.75-3.69)/3.69*100%=1.62% 3.75 is the experimental value from two parallel capacitor schematics. Mathematically, discharging capacitor takes infinite amount of time but 5 seconds for engineers. Time constant tao represent time system for significance of charge




RC system data deriving equations

Quantitative analysis was used for studying the RC system. The goal was to derive equation that describes the mathematics relationship between voltages across capacitor and time which describes the delta voltage as the capacitor discharges.

In the beginning, the voltage across the charged capacitor was measured. Also, the circuit, a current meter, LoggerPro and a resistor were all attached to the closed circuit. Data was gathered and a Potential vs. Time graph and a Current vs. Time graph was made. As seen in the LoggerPro graphs below, there are a total of four graphs; potential and current graphs for with voltage and potential and current graphs for without voltage. A best fit line was made for each of the graphs with the equation Ae-ct + B. The analysis of the formula can be seen in the unit analysis photo below. It can be concluded that the relationship between potential/voltage and time for a charged capacitor is VC=Vmax (1-e-t/RC) and for a discharged capacitor it is VD=Vmax e^(-t/RC). By showing the linear fit through the equations experimentally received, there is high correlation which means observed decay curve fit theory with equation of Q(t)=Qmax(1-e^(-t/tao)).

Potential and current vs time graphs

2nd Potential and Current vs Time Graph with higher correlation values.