What is a capacitor used for?
Capacitors are electrical devices used to store energy
Define capacitance:
Capacitance is defined as the charge stored per unit potential
What forms do capacitors come in?
Capacitors can come as isolated spherical conductors or two parallel plates
How can an isolated spherical conductor act as a capacitor?
An isolated spherical conductor acts as a capacitor as it can store charge on its surface
An isolated spherical conductor can store charge on its surface, which means it can act as a capacitor
When the conducting sphere is connected to a high-voltage supply:
electrons move on to, or off of, the surface of the sphere
the remaining charges are of the same type, so they repel
the surface is conducting, allowing them to move and become evenly distributed
How do parallel plate act as a capacitor?
A parallel plate capacitor is made up of two conducting metal plates connected to a voltage supply
The negative terminal of the voltage supply pushes electrons onto one plate, making it negatively charged
The electrons are repelled from the opposite plate, making it positively charged
There is a dielectric between the plates which ensures charge does not flow freely between the plates; The ‘charge stored’ by a capacitor refers to the magnitude of the charge stored on each plate in a parallel plate capacitor or on the surface of a spherical conductor. The capacitor itself does not store charge.
How do you calculate capacitance?
C = Q / V
Capacitance C is measured in farads F
What is the equation for capacitance of a spherical conductor?
V = Q / 4πe0R = Q / C
C = 4πe0R
The charge Q is not the charge of the capacitor itself, it is the charge stored on the surface of the spherical conductor
What is the formula for capacitors in series?
1/C total = 1/C1 + 1/C2 + 1/C3 …
Derive the formula for capacitors in series:
What is the formula for capacitors in parallel?
C total = C1 + C2 + C3 …
State the relationship between the charge and potential difference of a capacitor:
For a capacitor, its charge ∝ the potential difference across it - Q ∝ V
What does a Q against V graph look like?
A Q against V graph is a straight-line graph cutting through the origin
- The gradient is equal to the capacitance of the capacitor
- The area under the graph is equal to the electric potential energy stored in the capacitor or the work done in charging the capacitor
How do you calculate the electrical potential energy or the work done stored in a capacitor?
W = (1/2) * QV
If the charge is substituted using Q = CV, the work done is also equal to:
W = (1/2) * CV^2
Or
W = Q^2 / 2C
How do capacitors discharge?
Capacitors are discharged through a resistor - the electrons flow from the negative plate until there are equal numbers on each plate
What happens when a capacitor discharges?
As a capacitor discharges, the current, the potential difference and charge all decrease exponentially over time - hence the graphs of their variation with time are all identical and represent an exponential decay
How is the rate at which a capacitor discharges affected?
The rate at which a capacitor discharges depends on the resistance of the circuit:
1. If the resistance is high, the current will decrease and charge will flow from the capacitor plates more slowly, meaning the capacitor will take longer to discharge
2. If the resistance is low, the current will increase and the charge will flow from the capacitor plates quickly, meaning the capacitor will discharge faster
Define the time constant for a capacitor:
The time taken for the charge, current or voltage of a discharging capacitor to decrease to 37% of its original value; it is essentially a measure of how long it takes for a capacitor to discharge and is a useful way of comparing the rate of change of similar quantities such as charge, current or potential difference
The proper definition is the time taken for the charge of a capacitor to decrease to 1/e of its original value where 1/e = 0.3578
What is the time constant equation?
τ = RC
τ = time constant (s)
R = resistance of the resistor (Ω)
C = capacitance of the capacitor (F)
What is the general capacitor discharge equation?
X = X0 * e^-( t/RC )
X = current, charge or potential difference
X0 = initial current, charge or potential difference before discharge
e = the exponential function
t = time (s)
RC = resistance (Ω) × capacitance (F) = the time constant tau (s)
Derive the formula for capacitors in parallel:
