A-Level – Capacitors

Contents
– Intro to Capacitors
– Relevant basic equations
– Capacitors in series and parallel
– Charging and discharging a capacitor
– Practice equations

What is a capacitor and what is it’s purpose?

A capacitor consists of two parallel conducting plates separated by an insulating (dielectric) material. A capacitor is an electrical component which has the function of storing energy in the form of an electric field.

Equations

E = V*d

E = Electric field strength
V = Voltage
d = Distance between the conducting plates

C = Q/V

C = Capacitance
Q = Charge stored on the conducting plates
V = Voltage

Q = (Eo*A)/d

Q = Charge stored on the conducting plates
Eo = Permittivity of free space
A = Cross-sectional area of the conducting plates
d = Distance between the conducting plates

Capacitors in series and parallel

Capacitors can be arranged in series or in parallel to eachother in an electrical circuit. Depending on how they are arranged we can use two equations to calculate the overall capacitance of the circuit.
When capacitors are in series and parallel the following equations can be used to calculate the total capacitance:

C = 1/[(1/C1)+(1/C2)+…] (Series)
C = C1+C2+… (Parallel)

C = Total capacitance
C1, C2, … = Capacitance of each individual capacitor

Charging and discharging a capacitor

When the concept of charging and discharging arises, it is best to think about it in terms of the flow of electrons.
When a capacitor is charging at a high rate, the electrons are flowing onto the conducting plate of the capacitor very quickly. Likewise when a capacitor is discharging at a high rate, the electrons are flowing off of the conducting plate of the capacitor very quickly.
However, if the capacitor is charging at a slow rate, the electrons are moving onto the conducting plate very slowly. Hence, when a capacitor is discharging at a slow rate electrons are moving off the plate slowly.

When a capacitor is fully charged the maximum amount of electrons are squeezed onto the conducting plates of the capacitor, this would imply that no more electrons can fit onto the plates so it cannot be charged up further.

When a capacitor is fully discharged zero electrons are found on either plate of the capacitor. Hence, no more electrons can leave the conducting plates of the capacitor as there are no electrons present, therefore the capacitor won’t discharge any further.

Charging and discharging a capacitor through a resistor

The idea of placing a capacitor and resistor in an electrical circuit together, allows us to control the rate at which the capacitor can be charged/discharged.
This is because of the equation:

Q = Qo(1-exp[-t/CR]) (Charging equation)
Q = Qo*exp[-t/CR] (Discharging equation)

Q = Charge stored on the conducting plates
Qo = (C*V) = The maximum amount of charge that can be stored on the conducting plates
t = Time the capacitor has been charging for
C = Capacitance
R = Resistance of the resistor placed in the circuit

Practice questions

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