Capacitors
I need to cover capacitors before I move on to circuits. Capacitors store electric potential energy. When a capacitor is hooked up to a battery, the electrons will be repelled from the low potential side and congregate on one of the capacitor plates. Similarly, protons will be repelled from the high potential side of the battery and move to the other capacitor plate. Charge will continue to move until the potential difference of the parallel plates equal the potential of the battery.
The maximum charge that a capacitor can obtain is Q=CV where Q is the charge, C is the intrinsic capacitance, and V is the voltage (potential). Although you can solve for C, the charge and voltage will not affect the capacitance. The equation for capacitance is C = Ke(A/d) where “e” is a constant, A is the area, d is the distance between two plates, and K is the dielectric constant. Don’t forget that area is pi*r^2
The dielectric constant is a pretty important topic. If you look at the relationship of C and K, you see that they are proportional to each other. The stronger the material, the higher the capacitance is. A dielectric works by disrupting the electric field. The molecules in a dielectric will polarize causing an electric field in the opposite direction. The net Electric field will therefore be smaller.
Now, what happens if we charge a capacitor with a battery and then remove the battery? Well, the charge will have no more movement meaning it will be constant. Since Q = VC, since Q is constant and the capacitance increases, the voltage will decrease. Similarly, V=Ed. If voltage decreases, the electric field will decrease. The potential energy is 1/2QV, 1/2CV^2 or Q^2/2C. Since V decreases and C increases, the potential energy will decrease.
Things will be different if we keep the battery connected after the capacitor is fully charged. The voltage will increase causing Q to increase. Since V=Ed, the electric field strength will be much larger, negating the fact that dielectrics usually decrease an electric field. Similary, Since E increases, the potential energy stored will increase as well.
Lastly, when a capacitor is charged, it will increase it’s voltage exponentially and slowly level off. When a capacitor is discharged, it will quickly lose charge and slowly go to zero
