Capacitor (16th Day)

Spring 2015
Professor Mason
April 28 Class

Circuit Calculation in Quiz

First thing we did in class was a quiz about calculating V, I, R, and Power in a circuit. R1 and R2 were given; in order to find both I1 and I2, we had to use loop formula, which was equation 1: [E1 - E2 + 320 I2 = 0] and equation 2: [E2 - 510 I1 - 320 I2 = 0]. By plugging in the numbers and substituting the variables, we got I1 equals to 0.037 A, I2 equals to -0.022 A, and I3 equals to 0.059 A. After we finished calculating the I, we could use [V = IR] formula in order to get the V. After we got all the R, V, and I, we could finally calculate the power by using [P = IV] or we could simply say [P = I^2 R]. Then, the total P is just P1 + P2 (J/s).

Capacitor

When a capacitor is attached to a battery, it acts similar to the battery; the positive charge and negative charge are attracted to each other. As shown in the picture attached above, if the battery is attached to a capacitor, [Vb = Vc]; it means that the voltage unit in the battery is the same as the capacitor. If no battery is attached, there is no flow going through the circuit; thus, when we attach a light bulb in the circuit, there would be a flow going through the bulb, and it will make the bulb light. Capacitor is defined as an equation of [C = Q / V], which C is the capacitor, and Q/V is the stored charge per voltage unit. C is defined with a unit of Farad, Q is defined with a unit of Coulomb, and V is defined with a unit of Voltage. Stored energy has a definition of [delta U = Work = Integral of V dq = Integral of Q/C dq = Q^2/2C]. [Q^2/2C] could also be simplified to [CV^2/2]. If the area of the capacitor is increased, the capacitor is also increased, which means that Area is perpendicular to Capacitor. It also happens with distance; the shorter the distance is, the larger the capacitor is, which means that C is perpendicular to 1/d. 

Capacitor experiment

In class, we needed to do an experiment that involves two sheets of aluminum foils, a book, and something heavy to push down the book and capacitor so it would measure accurately. First, we need to place two sheets of the foils in between the book pages; then, we put the positive and negative charges of the machine and put it to the foils, so that it would measure in terms of nano Farad (nF). The data we received were written in the book, and these are the data: (1 page = 1.22 nF, 3 pages = 0.8, 5 pages = 0.68, 7 pages = 0.63, 9 pages = 0.54, 11 pages = 0.52, 13 pages = 0.47, 15 pages = 0.44, and 17 pages = 0.41 nF); 1 page is equal to 0.078 mm. The graph is shown in the picture attached above. 

We could also calculate the capacitor using [C = k Eo A / d], which k comes from [Epsilon = k Eo], and k is the permittivity (permittivity of paper is 3.5); Eo is the constant. Paper does not have the same permittivity as air, so it would have different value when the distance between two capacitors are filled with air. 

The calculation shown in the picture above is the formula to calculate the area if k, Eo, C, and d are given; Eo and k would be different depending on the material we use. 

 For the calculation part, we were given this picture shown on the left; we needed to find the C and the V given that the charge (Q) in series setup is equal to each other. C in series setup is the same as R in parallel setup and vice versa. For the picture on the left, we first needed to find the charge in C2 because it equals to the charge in C1; then we could find the voltage C2. Therefore, we could find the V in  battery.  For the last picture, we found out that we could find the work done using[1/2 CV^2].

Capacitor in different kind of functions

In class, we found out that the definition of electric field around capacitor is equal to [E = V/d], which V is the voltage unit, and d is the distance. For spherical Capacitor, the equation for it is [C = (R1 R2)/ (k (R2 - R1))]. Next in class, we discussed about dielectrics strength and constant; the unit of dielectrics strength is (V/m), and the constant is [k = E/Eo]. Finally in class, we needed to measure the C value for each capacitor, with two capacitor given. The measurement was parallel = 2.11 uF, series = 0.52 uF, and each of them has 1.06 uF; therefore, we found out that parallel setup is just the sum of both capacitor, and series setup is the half value of individual capacitor.