Capacitors Article: Capacitors & Capacitance

Capacitors Capacitors Article: Capacitors store energy by holding apart pairs of opposite charges Therefore, charge on the plates Q = CV (where C is the capacitance, which is how much of a charge difference the capacitor holds when a certain voltage is applied) 1 E = 2 𝐶𝑉 2 Capacitors do not store charge, they store an imbalance of charge (net charge of both plates is always 0) The further two plates are, the less the other plate’s electrons feel the repulsion (capacitance of plates will be inversely related to plate separation If the area is larger, then adding charge to the capacitor makes it easier and is therefore capacitance is directly related to area There: 𝐶 = !0 " # where ε0 = 1/(4kπ) A is the area of the plates, ε is the permittivity constant (determines how easily the air between the plates allows an electric field to form) Dielectrics Article: Dielectrics are materials that don’t allow current to flow (often called insulators) and even though they don’t flow When you place a dielectric substance in the gap of a parallel-plate capacitor, it increases the total capacitance (Cwith dielectric = kCwithout dielectric) The higher the k value is, the better a material functions as an insulator and therefore increases the capacitance of the capacitor, decreasing the electric field inside of the capacitor Remember, Q stays constant if the battery is disconnected first and therefore the introduction of the dielectric material will decrease the V by whatever factor the Cwith dielectric is Remember, V stays constant if the battery is still connected to the capacitor, and therefore the introduction of the dielectric will, the difference in charge will increase by the same factor as the Cwith dielectric went up by Capacitors & Capacitance: Even if the capacitor plates are different sizes, they both store equal and opposite charges Capacitance tells you how good that capacitor is at storing charge C = Q/V which is in units of C/V or F (Farads) Capacitance is stationary because you need to alter the distance or area between the two plates in order to change it Energy of a Capacitor: When a capacitor is charged up, it not only stores charge but also energy (form of electrical potential energy) which can be used to generate current (and light up a lightbulb) 1 1 !2 E = 2 𝑄𝑉 = 2 𝐶𝑉 2 = 2" for the potential energy of a capacitor and is because as additional electrons go back to the positively - charged plate, the voltage drops over time (use the ones where you KNOW two variables) If you have C in the formula you can “see” the V2 (helpful way to remember) V is only the same as the battery if the capacitor was fully charged (so a whole bunch of capacitors in sequence/parallel, you need to find the voltage across that specific capacitor Capacitors in Series: (Ceq)-1 = (C1 + C2 + ...)-1 ← For capacitors in series For capacitors in series, charge on every capacitor in series is the same Sum of the voltages of capacitors in series will equal the voltage of the battery Vtot = Q/C1 + Q/C2 Capacitors in Parallel: The voltage drop across capacitors in parallel have the same voltage drops Charges for capacitors in parallel are not the same Ceq = C1 + C2 + ... Also, you can add up the charges on the capacitors in order to come up with Qtot Dielectrics in Capacitors: A dielectric material, like paper, will be placed in between the two capacitor plates in order to 1. Keep them from touching and 2. Increases the capacitance of that particular capacitor and therefore decreases the voltage (since charges in the dielectric are canceling some of it out) If you leave the battery connected, you can supercharge the capacitor plates since the voltage decreased, the battery keeps charging the capacitor plates Dielectric constant for an insulating material is always greater than 1 since it always increases the capacitance Extra Notes: When the battery and dielectric material are taken out of a circuit and the charges are allowed to redistribute, then the charges will equilibrate on all capacitors, even though some had the dielectric material originally