Capacitance & Decay

This image shows how we were to solve for current, voltage, resistance and power on our quiz. We used the looping method, Kirchhoff's Laws, and formulas for voltage and power.

A capacitor is a device that stores electric charge and electrical potential energy.

Capacitance is the measure of the ability of a device to store charge per unit of voltage applied across the device. It is a measure of the net charge per unit voltage.

The formula for capacitance between two charged plates is derived below.

Here is picture of a capacitor we used.

The formulas for capacitance in series and parallel circuits is as shown. We used the multimeter to find the capacitance of each capacitor.

In this problem, we solved for the total capacitance in a parallel circuit. The formula is similar to that of resistances in a parallel circuit.

Here we solved another capacitance problem. We also solved for the energy stored inside of the capacitor and its charge.

Capacitance of capacitors in series can be solved using the following formulas.

Capacitance of capacitors in parallel can be solved using the following formulas.

Similar to reducing resistances, we can reduce capacitance using the following method:

Formulas for finding voltage, current, resistance, capacitance, and charge in series and parallel circuits are shown below. 

In the next activity, we measured the change in capacitance at different separation distances. We placed two pieces of foil in different sections of our lab book and measured the capacitance using a multimeter.

From these measurements, we made the following calculations and graphs of capacitance vs separation distances.

The graph was displayed on logger pro and fit equation was found. As the separation distance increase, the capacitance decreases.

Here we used the capacitance formula and the separation distance to solve for the area of the capacitor's plates.

Below is a graph of current vs time for a discharging capacitor. The voltage, charge, and current of a discharging capacitor can be found using the formulas below. 

A capacitor charging will have an increase in current over time lapsed. when the current decreases, the charge decreases. The formulas below can be used to solve for charge on a capacitor as well as the current and voltage.

Below is a description of how a light bulb will react when it is connected to a capacitor in series with applied voltage. There is also a description of how a light bulb will react when there is no battery connected and only a capacitor.

The derivation for the theoretical decay curve is shown below.

In the RC circuit problem below, we solved for the time constant and time required for the capacitor to discharge to one electron.

Summary:

• A capacitor is a device that stores electric charge and electrical potential energy.
• Capacitance is the measure of the ability of a device to store charge per unit of voltage applied across the device. 
• It is a measure of the net charge per unit voltage.
• A capacitor charging will have an increase in current over time lapsed. when the current decreases, the charge decreases. 
• We can simplify capacitance in a circuit problem similarly to that of resistance.