Capacitors

The correct solution for the quiz on Kirchhoff's Rules. We see that that current passing through the top resistor is split up between the middle resistor and the lower source. The negative result for I2 means that the direction is in the opposite direction of our assumption.

In order to observe capacitance, we inserted different amounts of pages, each 0.095 mm thick, in between two sheets of foil paper in order to see how the separation alters the capacitance.

We see that the more pages that are in between the sheets of foil, the capacitance goes down, while implies an inversely proportional relationship. Also, if we were to increase the area of the sheets of foil, the capacitance would increase. 

Here is a graph for the thickness of the space between the sheets of foil paper as a function of capacitance. The inversely proportional relationship is clearly visible.

In order to increase the capacitance of a capacitor, a dielectric can be inserted in between two conducting plates. This induces a charge that lowers the voltage in between the plates. The charge on the actual plates however remains constant. The constant k multiplies by the permittivity of free space equals the permittity of the dielectric. 

The equivalent capacitance of a circuit with capacitors in parallel is the algebraic sum of each capacitor. Capacitors in series create an equivalent capacitance in a behavior similar to resistors in parallel.

The top circuit in the top left corner is the equivalent of the circuit drawn in blue in the lower left hand corner. Drawing this circuit like this simplifies our calculations. Using what we know from the previous picture, we are able to find the equivalent capacitance of the circuit. The charges present on capacitor 1 and 2 are equal and less than the charge present on capacitor 3.