Day 19 Charge Buildup and Decay in Capacitors

At the beginning of the class, we did an experiment called charge buildup and decay in capacitors.

We made a circuit of battery, a capacitor, and a switch in series. The bulb gets dimmer and dimmer as the switch is closed more. Then we take away the battery out of the circuit and the bulb lit again and got dimmer after times.

This graph shows the brightness of the bulb as the time went up when it is placed across a charged capacitor without the battery. We can see that the bulb is less bright overtime.

In these two pictures, we did an activity where we hooked up two capacitors to 2 batteries with different voltages and measure the capacitors' final voltages. And we found that Vtot= 1/2(V1+V2).

In this picture, we did an experiment called quantitative measurement on an RC system. We built a RC system with a battery, a capacitor, a resistor, a voltage measuring lead, a computer, and 6 wires.

This is the voltage vs. time graph we made by logger pro about two processes, charge the capacitor (red) and discharge the capacitor (blue)

We used the equation V=IR and Q=CV to find the unit of RC, so the unit is second.

We used the equation V=Q/C, V=IR and I=dq/dt = -q/RC to find that q = e^(-t/RC)

This is an experiment where the two wires together will explode if turn on the green box.

In this picture, we graphed I vs. t graph by analyzing the V vs. t and brightness vs. t graphs.

We did a practice problem on RC circuit. There are two equation, one is for charge, the other is for dischage.

Then, we found the RC is 1s and another loop's RC is 0. Then we used the equation of charge to find that t is 1.1 second.

In this picture, the switch is turned off, and we used the equation of discharge to find the time is 149s.

Conclusion

In today's class, we did a few experiments and activities on ideas of charged capacitor, discharged capacitors, and RC circuit in order to understand how they work. We also learned to find RC and time constant in a RC circuit.

Day 18 Capacitors and Capacitance

At the beginning of the class, we did a quiz about Kirchhoff's law. Our task is to final R,V,I, and P in a circuit.

After the quiz, capacitors and capacitive circuits were introduced to us

And we found that the work done by capacitor is 1/2 V^2*C where C is the capacitance.

Then we did an activity to predicting dependence on area and separation which we measure the thickness and the capacitance of pages of a book and graphed D (thinkness) vs. C (Capacitance)

We then did an activity to write an expression for capacitance as a function of ke₀dA. where e is the permitivity. We got C = ke₀dA/d

We did a problem on finding the area and the side length of a capacitor. 

Then, we are given two capacitors and asked to find total capacitance. If the capacitors are in series, we use 1/C1+1/C2 = 1/F. If they are in parallel, we use C1 + C2 = F

Therefore, we did a problem on finding total capacitance.

Also, we find the total work by battery by the equation 1/2 cv^2.

Conclusion

In today's class, we started off by taking a quiz on circuit problem, then we started discussing about capacitor and capacitance and its applcations. We did a lot of problems on capacitance and derived some equation. We also learned to find the work of battery if we know the capacitance.

Day 17 DC circuits

At the beginning of the class, we need to predict what happens if the switch is turned on in this circuit problem.

Our predictions were that #1 and #2 bulbs will stay the same and #3 bulb will stay off.

This picture shows that our prediction was right, #1 and #2 bulbs stayed the same as the switch is turned off because the voltage is the same. And #3 bulb is not on because the voltage is 0.

This is another practice exercise on circuit, we predicted that two bulbs will be the same as the switch is on.

As a result, our prediction was right because on the top bulb there is a parallel battery so the voltage of the two side does not change. And for the bottom bulb, the parallel battery has no effect on it. So it stayed the same.

In these two picture we were performing an activity where we tried to arrange the circuit to control the bulb to be bright or dim. And we found that we should make the bulbs parallel to make the bulbs brighter.

In this picture, we practiced four problems on circuit.

First: 

We made the circuit as drawn on the top left corner, and we found the voltage of source = Vr1 + Vr2.

Second:

For the second circuit we measured the voltage of source and the current of source Ir1 and the current of Ir2 and Ir3, and we found that Ir1 = Ir2 = Ir3.

Third:

We made the circuit as drawn as the top right corner. The two resistors are place parallel, and we measured that the voltage is Vr1 = Vr2.

Fouth:

We measure the current of the source I1 and the two resistance Ir1, Ir2, and found that I1 = Ir1 + Ir2.

In this picture, it shows 4 different kinds of colors in one resistor. The first three are certain which we can measure their resistance R, and the last one is the uncertainty of R.

We predicted the 4 different resistance and their uncertainties. The resistance is not good.

In this picture, all the resistances are the same as 620 ohm, and we calculated that the different R of 4 graphs.

In this picture, we calculated the total R of the circuit by using the laws of parallel and series.

This picture shows the last exercise we did, we used the Kirchhoff's Law to solve this problem.

Conclusion

In today's class, we have looked at two different arrangement parallel and series on a DC circuit and the relationships between voltage, current, and resistance. We also learned Kirchhoff Rule and the Loop Rule to apply on the problem so we are able to solve the circuit problems by calculating the amount of current flowing through a circuit, and total resistance whether the circuit is in parallel or series arrangement. 

VPython: Electric Potential

Final Display

Code

This activity is to practice calculating the electric potential using the VPython. I created total three charges. One is positive and two are negative. And I created eight points on a ring which surrounding the charges. It turned out the electric potential is larger when the point is closer to the positive charge, and it is smaller when the point is closer to the negative charges. The electric potentials of each point of the ring are shown on the first graph.

Day 16 Potential of Continuous Charge Distributionsb

At the beginning of the class, we first started off by estimating the potential from a charged ring. We got that V = kq/r and r is square root and a^2 + b^2 in this case.

In this case, r is sqrt(x^2+4a^2), another is sqrt(2a^2+x^2)

We also found the angle's relationships with a and x. 

We plugged in the previous equation and got V(θ) = kqcosθ/x

We also used excel to find the total potential energy of the charged ring, which the ring is divided into 16 parts. To find the total potential energy, we need to added everything up.

In this picture, we did the actual calculation for calculating the total potential energy. And the result is the same as the excel's.

We used the equations in the picture to find the equation of Ex = KQx/(x^2+a^2)^3/2

We also found that ΔV = KQ/sqrt(x^2+a^2)

We did a problem to calculate the electric potential due to a finite length line-charge.

We used the equation we derived previously and calculated the electric potential.

Then we used excel to calculate the same result.

These three pictures shows the equipotential surfaces where we drew perpendicular lines.

Electric Potential Lab




The pictures above are the equipment we used in this experiment. We used them to measure different voltages at different positions to calculate the Δv/Δx.

Pictures above are the data we recorded during the experiment.

Finally, we used excel to find Δv/Δx.

Conclusion

In today's class, we did various problems on finding electric potential in different cases. We also learned that using excel would be an easier and faster way if there are too many parts in a charged bar. We also learned about equipotential surfaces and did a lab on electric potential.