Day 19: Charge Buildup and Decay in Capacitors

  First, we did an experiment called charge buildup and decay in capacitors.

  We made a circuit by battery, capacitor and switch. The bulb gets dimmer when the switch is closed more. If we take the battery about and the bulbs starts getting dimmer.

  As the time goes long, the bulb is dimmer and dimmer.

  In this experiment, we connected two capacitors with 2 different voltage batteries. Then we need to measure the capacitors'final voltage. We found V=1/2(V1+V2).

  Then we did another experiment. We used battery, capacitor, resistor and voltage measuring lead, a computer and wires to built a RC system.

  This is a voltage vs. time graph we made by using Logger Pro.

  We found the unit for RC by using V=IR and Q=CV.

  Then we found the equation q=e^(-t/RC) by using V=Q/C, V=IR and I=dq/dt = -q/RC.

 When the green equipment turn on, there will an explsion in the wires.

  We graphed I vs. t graph by analyzing brightness vs. t graphs and V vs. t.

  This is an exercise problem we did during the class. There are two equations one is for charge and the other is for discharge.

  We used the equation of charge and found time is 1.1 second.

  We used equation of discharge to found the time is 149 s.

Conclusion:

  At beginning of the class, we did an experiment called charge buildup and decay in capacitors. We found how it works and how it affect the circuit. Then we did another experiment about the RC system. We found some useful equations to calculate time.

Day 18: Capacitors and Capacitive Circuits

  First, we did a quiz about Kirchhoff's current law and Kirchhoff's voltage law to find three voltage, three current, three power and total power.

  After the quiz, we started to learn capacitance - store charges. The unit for capacitance is F and symbol is C. We know Q(charges)=V(voltage)*C(capacitance), so we could find the equation for work is W=(1/2)V^2*C.

  Then we did an experiment. We measured the capacitance of different pages and thickness of a book, then we made graph by using Excel and find a new equation C=k(constant)/d(thickness).

  In this photo, we found area, distance and permittivity can influence capacitance because the equation C=(kE0A)/d.

  We used equation to calculate the area.

  There are the equation we found to calculate series and parallel of capacitance.

  We used the equation we found above to calculate C.

  There is an exercise, and our answer for C is 52 nF.

  There is another exercise problem professor gave us to calculate by using the equations we found.

  We found the work done by battery if capacitors are charged by using 1/2CV^2.

Conclusion:
  At beginning of the class, we did a very surprised quiz. This quiz is not that hard but need lots of time to finish it. Then we started to learn capacitance and how it works in circuit. Then we found a equation for series and parallel of capacitance. After we did some interesting exercises by using the equations we learned before.

Day 17: DC Circuit Analysis

  There is a exercise professor gave us: two batteries, one switch and three bulbs. The question is what will happen if switch is on.

  According to the question, we believed first and second bulb will stay same but third bulb will off if switch is on.

After the switch turn on, the voltage on first and second bulb are the same as switch is off, that is the reason why this two bulbs stay same. However, the voltage on third bulb became zero, so third bulb is off.

  This is another exercise. Same question: what will happen if switch is on. And we predict the bulbs stay same.

  When the switch on, bulb 1 did not change because one battery is parallel on the bulb 1-the voltage of two side did not change. Bulb 2 stay same because the parallel battery did not influence the bulb.

  There are five different situations. If we make the bulbs series, then the bulbs will dimmer. If we make the bulbs parallel, then the bulbs will brighter.

  First situation: there are two resistant in series and same batteries. We used only one battery first time and make two batteries as series second time. Then we measured the voltage source and R1 and R2.We found voltage of source=Vr1+Vr2.
  Second situation: we need measure the voltage of source and current of source Ir1, Ir2 and Ir3 under same condition. We found Ir1=Ir2=Ir3.
  Third situation: we made two resistants parallel and measure the voltage source and the Vr1 and Vr2 of two resistants. We found voltage of source=Vr1=Vr2.
  Fourth situation: we need measure current of source I1 and resistants Ir1 and Ir2 under third situation. We found I1=Ir1+Ir2.

  There are four different colors in one resistant. First three are certain and we can measure R. However, the last one is the uncertainty of R.

  This is our prediction of the four different resistants and uncertainty. We found first one is bad.

  The resistants are 620 om, then we calculated the different total R of four graphs.

  We need to calculated the total R of the circle. In series, R=R1+R2+... in parallel, R=(R1*R2*..)/(R1+R2+..).

  There are three equations for three different values to calculate.

  Conclusion:
  Today, we did many interesting exercises and experiments. First, we need to predict the condition of bulbs if the switch is on. And our prediction is correct. Second, we did another predict with same question. Luckily, our prediction is correct again. Then we did some experiments to calculate the resistant and figure out some useful relationships and formulas.

Vpython Homework

Day 16: Potential of Continuous Charge Distribution

  This is the equation we found for the electric potential energy.

  Then we used same equation V=kq/r found another potential energy. One is on top and the other one is at the middle of the ring.

  There are the three equations for theta.

  We found a new equation V=kqcostheta/x.

  We used Excel to found the total potential energy by using the equation V=kq/r.

  We found the total potential energy which match our excel answer.

  We used the potential energy V to find the electric field.

  Then we use intregration to found the change of the potential energy V.

  We calculate the potential electric energy of a point.

  We used the equation on the top to found the potential electric energy.

  We used Excel to the potential electric energy, the answer on the Excel is same as our calculate.

  There is a particle has positive charge. We draw the points which have the same potential electric energy.

  We have positive charge on the left and negative charge on the right.We draw the surface that has same potential electric energy.

  There is a electric dipole that draw on the surface.

  We used power supply, voltmeter and conductive paper to found different distant.

  We use Excel to found different voltage and change of V/x.

Conclusion:
  At beginning of the class, we found three ways to found potential difference at two points. Then we calculate the potential from a charge ring using the intregration. The equipotential surface is very important to analyze potential. Also, we did some exercises to found potential and used Excel to verify our answer.