Capacitors in Circuits 10/23

Today we learned that a capacitor is a device that stores electric charge and electric potential energy.
We defined capacitance as the measure of the ability of a device to store charge per unit of voltage applied across the device
C=Q/V

we learned that for capacitor in series the charge is conserved and that capacitors in parallel have the same voltage drop across one another.

we also proved theoretically by using the definition of current flow and relating it to capacitance that qc= q0 e(-t/RC), and V=Vo e^(-t/rc)

Here we have applied a best fit to the graph and shown experimentally the rate at which capacitors discharge and charge. Where the constant C is equal to 1/rc.

Kirchhoff's Laws

First we tested Current and voltage for parallel and batteries in series. From this we were able to prove Kirchhoff's rules. But Before we started to measure we had to learn how to measure we were given ammeters and taught the notation for voltage(AC and DC), resistance (ohms) and Current (DCA amd ACA)

This is the derivation for Kirchhoff's rules in series and in parallel.

Next we were thought how to read resistors and how to calculate or see their uncertainty.

Here is an example problem using Kirchhoff's rules, things to keep in mind for Kirchhoff's rules are looking at the junctions (where wires meet) and to set you loops and current in a closed of circuit. It is also good to now that current our is the same as current going in for batteries.

Lab

Electric Potential Energy

Here we drew a few diagrams of circuits with light bulbs in series and parallel; From experimentation we found that the bulbs were brightest when the bulbs were parallel and the batteries were in series. we found them to be least brilliant when the batteries were parallel and the bulbs were in series. We also discussed switches and described what pole and throw are.

Here we define voltage as potential energy over q and we described potential energy lines.

This formula relates electric potential difference with potential energy work and the formal definition of work.

Circuits

Today, we were introduced to circuits, we were thought how circuits are similar to rivers. First we had current, the flow of the electric charge measured in amperes. Then we had voltage, the electrical potential difference measure in volts. Then we found power, the ability to do work in watts. Next we went on to define Resistance as opposition to the passage of the electric current in ohms.

Here we define the current density (J), or current per cross sectional area (I/A) measure in amps/meter^2. Vd= delx/delt, I=delQ/delt. pn or charge density, charge/density. I=pn*Volume*q/delt. Therefore I=pnA (Vd * t) q /delt = pn*A*Vd*q
Note used on hw:(Finally J= I/A=pn*A*Vd*q/A = n*Vd*q.)

At the end of today we looked at wires and how their thickness effects the flow of electric charge (I). 

Electric Field Lines and Flux

E=kq/r^2 is proven to be true for point charges and spheres.

The surface are of a cylinder as well as its charge ratio.

Here we go ahead and find the electric field of a cylinder that is infinitely long.

Comparison of gravity to electric field

Flux and Gauss Law

Introduction, Today we learned about Gauss Law. We learned that flux = E.A or flux is equal to the closed surface integral of the electric field dotted with dA (the areas that makes up the entire surface)

or the charge enclosed over some constant epsilon not(q/epsilon). 

Note net electric force is always the same anywhere in the field defined so we can relate F=qE=ma

Here we have two charges to which we find the electric dipole moment, which is similar to moment of inertia. So what we did was let F= qEsin(theta) and then say r= d/2. so torque is F(d/2) + F(d/2), or qEdsin(theta) or pxE. potential energy is qrE. (think m=q, h=r, E=g)

In conclusion the Flux is dependent on the surface area or area perpindicular to field and the strength of the field or E.A. The electric dipole moment can be said to equal pxF.