Chapter 23 - Capacitors Flashcards
What is a capacitor?
Device designed to store charge
How does a capacitor work?
Two parallel metal plates placed near each other and connected to a battery. Electrons move through the battery and are forced from it’s negative terminal of the battery onto one side of the plates. An equal number of electrons leave the other plate and return to the battery via its positive terminal - so each plate gains an opposite and equal charge.
Draw the symbol for a capacitor
How do you calculate the charge,Q, on a capacitor when charging
Q = It where t = time after switch is closed
How can a capcitor’s pd be measured when charging?
By using a high resistance voltmeter in parallel with the capacitor and using the variable resistor to keep the current constant, either:
- Use a stopwatch and measure reading at measured times
- Use a data logger
What would a graph of charge against pd graph for a capacitor look like?
Straight line passing through the origin
Define capacitance and give an equation
The capacitance (C) of a capacitor is defined as the charge stored per unit pd
C = Q/V
unit: Farad (F)
How is the energy stored in a capacitor obtained from a graph?
Charge against pd graph
Area under the graph = energy stored = 1/2QV
as energy stored is equal to the work done to force charge on to the plates
Why does a capacitor store energy as it’s being charged?
Electrons are forced onto one of the plates and taken of the other. Energy stored as electric potential energy
What is the equation for the increase in energy stored when the seperation of two parallel plates increases?
1/2 QE delta d
where d = seperation between the parallel plates
Why does energy stored increase when seperation distance between the parallel plates is increased?
Work is done to force plates apart, overcoming the electrical attraction between the 2 plates.
Draw the graph for a discharging curve of charge against time
In what proportionality does current, charge and pd of a capacitor decrease with respect to time when discharging through a fixed resistor?
Exponentially
What actually happens in a discharge circuit?
- as soon as switch is closed, ‘large’ current flows and p.d. across capacitor drops
- as charge flows from one plate to the other through the resistor the charge is neutralised and so the current falls
- rate of decrease of p.d. also falls
What is the equation for the fractional drop in charge during the discharging process?
delta Q/ Q = - delta t/CR
What is the equation for the exponential decrease in charge with respect to time for discharging?
Q = Qo e-t/RC
What does the gradient of the tangent to the curve at a point on a Q-t graph give?
The current at that time
On a current-time graph, what does the area underneath the curve give?
Charge stored
What is the time constant of a circuit?
RC
where R = resistance of circuit and C = capacitance
At time t = RC after the start of the discharge, the charge falls to 0.37 (e^-1) of it’s initial value
unit: seconds (s)
When t=2RC in a capacitor’s discharge, what percentage charge remains?
14%
At what point, is a capacitor considered discharged?
When t=5RC
When is a capacitor fully discharged?
When the charge on the plates is zero and the current and p.d. are also zero
How do you know when a capacitor is fully charged?
Pd is equal to the source pd
Current is zero because no more charge flows in the circuit
Draw a charging curve for a capacitor through a fixed resistor for charge against time
How can you increase the charge stored on a capacitor?
Inserting a dielectric between the plates
What are dielectrics?
Electrically insulating materials materials that increase the ability of a parallel plates to store charge
Increase charge stored in a capacitor for any given pd. So increases capacitance of capacitor
How does a dielectric increase the charge stored in a capacitor?
When a dielectric is placed between two oppositely charged parallel plates connected to a battery, each molecule in the dielectric becomes polarised (electrons pulled slightly towards the positive plate). Surface of dielectric facing the positive plate gains a negative charge As a result more charge is stored as:
- positive side of dielectric attracts more electrons from the battery onto the negative plate
- negative side of the dielectric pushes electrons back tot eh battery from the positive plate
What is the relative permittivity of a dielectric substance?
Ratio of charge stored with the dielctric susbstance t the charge stored without
Er = Q/Qo
where Qo is the charge stored at the same pd when the space is completely empty.
What is the relative permittivity of a substance also called?
dielectric constant
What is the equation for capacitance of a capcitor with a dielectric
C = AEoEr/d
where A is the surface area of each plate and d = spacing between the plates
What can large capacitance be achieved by?
- Making the area A as large as possible
- Making the plate spacing d as small as possible
- filling the space between the plates with a dielectric which has a relative permittivity as large as possible
Why do most capacitors consist of two strips of aluminium foil seperated by a layer of dielectric?
Makes capacitance as large as possible because area A is as large as possible and the spacing d is as small as possible.
Describe the procedure for measuring the relative permittivity of a dielectric substance
Place dielectric sheets of uniform thickness between two parallel plates insulated from each other by small pieces of suitable insulation. A potential divider is used to apply a constant pd between the two plates. The capcitor is repeatedly charged and discharged through a microammeter. The microammeter current reading is proportional to the charge gained by the capacitor each time the the switch charges it. The current is measured with the dielectric in place and with the dielectric replaced by small insulating spacers of the same thickness as the dielectric sheet . Relative permittivity of the dielectric = I/Io where I is the current with the dielectric present
Draw the circuit used in measuring the relative permittivity of a dielectric substance?
When does dielectric polarisation occur?
When a dielectric is placed in an electric field and the electric charges shift from the average equilibrium positions
What is the effect of dielectric polarisation?
- +ve charges are displaced toward field and -ve shift in opposite direction
- creates internal electric field that reduces overall field within dielectric so reducing p.d. across capacitor
What is the effect of an internal electric field in a dielectric?
It reduces the overall field within the dielectric itself, reducing the p.d. across the capacitor
How can the p.d. return to its original value after dielectric polarisation?
Requires the addition of more charge onto the plates
What effect does dielectric polarisation have on the capacitor overall?
The capacitor can store more charge for the same p.d. and increase its capacitance
