Capacitors Flashcards
What is meant by the capacitance of an object?
The capacitance of an object is the amount of charge it is able to store per unit potential difference across it.
What is the unit of capacitance?
Farads (F)
What is a capacitor?
A capacitor is an electrical component which can store electrical charge.
Describe how a capacitor works.
- Two parallel plates connected to a d.c. power source
- One plate becomes negatively charged and the other positively charged
- Plates separated by electrical insulator so no charge can pass between (potential difference builds up between them)
Describe the circuit needed to investigate V and Q using a capacitor.
- Battery connected to a variable resistor, connected to an Ammeter, connected to a capacitor, connected to a switch, connected back to the battery.
- Voltmeter across the battery
How could you investigate V and Q using a capacitor?
- Charge capacitor using a constant current
- Constantly adjust variable resistor to keep charging current constant for as long as possible
- Record the p.d. at regular time intervals until it equals the battery p.d.
- Plot a graph of fixed charging current against time taken to charge capacitor
What is the area under a charging current - time taken to charge capacitor graph?
The charge stored in the capacitor.
What do you get if you plot charge stored against p.d.? (using Q = )
A straight line through the origin - Q and V are directly proportional.
Give 3 examples of real world uses of a capacitor.
- Camera flash - camera battery charges the capacitor over a few seconds, then the entire charge is dumped into the flash
- ‘Ultracapacitors’ can be used in back-up power supplies
- To smooth out variations in d.c. voltage supplies
How can you find the energy stored by a capacitor?
By using the graph of potential difference against charge for the capacitor (area under it).
What are the 3 main equations to do with energy stored by capacitors?
E = 1/2 QV E = 1/2 CV^2 E = 1/2 Q^2 / C
What is meant by permittivity?
Permittivity is a measure of how difficult it is to generate an electric field in a medium. The higher the permittivity of a material, the more charge is needed to generate an electric field of a given size.
What is relative permittivity? What is relative permittivity also know as?
The ratio of the permittivity of a material to the permittivity of free space. (permittivity of material / permittivity of free space).
Also know as the dielectric constant.
What is a polar molecule?
A molecule with a positive end and a negative end.
What happens to polar molecules between the plates of a capacitor when an electric field is generated between them?
The negative ends of the molecules are attracted to the positively charged plate and vice versa. This causes the molecules to rotate and align themselves anti-parallel to the electric field.
Describe how a capacitor is charged in terms of electrons.
- Electrons flow from the negative terminal of the supply to the plate connected it (this plate becomes negatively charged)
- At same time, electrons flow from other plate to positive terminal of supply, making that plate positive
- These electrons are repelled by the negative charge on the negative plate and attracted to the positive terminal of the supply
- Equal and opposite charge builds up on each plate
What happens to the current when the capacitor is fully charged?
The current falls to zero.
What happens if you charge a capacitor through a fixed resistor?
The resistance of the resistor will affect the time taken to charge the capacitor.
Explain what happens to the p.d. and current when charging a capacitor through a fixed resistor.
- P.d. across capacitor is zero at first, therefore no p.d. opposing the current, meaning an initial high current from battery
- As capacitor charges, p.d. across it increases and p.d. across resistor decreases, and the current drops
- Charge on capacitor is proportional to the potential difference across it
Describe the I-t, V-t and Q-t graph when charging a capacitor.
- I-t graph - Starts at initial current and is a curve which decreases with a less and less negative gradient
- V-t graph - Starts at zero and is a curve which increases with a less and less positive gradient until capacitor is fully charged
- Q-t graph - Same as V-t graph
In the equation for charge of the capacitor at time t, what does each letter mean? (Q, Q0, t, R and C)
Q - charge of the capacitor at time t / C
Q0 - charge of the capacitor when fully charged / C
t - time since charging began / s
R - resistance of fixed resistor / Ohms
C - capacitance of capacitor / F
What is the equation for voltage across a charging capacitor and the charging current?
- Voltage equation is in the same from but with V instead of Q
- Charging equation - I = I0e^(t/RC)
How do you discharge a capacitor and why does it discharge when you do this?
Take the battery out of the circuit and reconnect the circuit. This discharges it because when a charged capacitor is connected across a resistor, the p.d. drives a current through the circuit which flows in the opposite direction from the charging current.
Outline an experiment which investigates capacitors discharging.
- First charge the capacitor
- Then open the switch, remove the power source, and add a voltage sensor across the capacitor and a data logger across the ammeter and voltage sensor
- Close switch and allow capacitor to discharge
- When ammeter reading reaches zero, use computer to calculate charge on capacitor over time
- Computer can then plot variety of graphs showing how current, p.d. and charge vary over time
- Can also create log-linear plot of results to produce straight-line graphs
Describe the I-t, V-t and Q-t graph when discharging a capacitor.
- I-t graph - curve starting at initial current and gradually decreasing to zero
- V-t graph - same as I-t graph but starts at V0 (p.d. across capacitor when fully charged)
- Q-t graph - same as other 2 graphs but starts at Q0 (charge of capacitor when fully charged
What is the equation for voltage across a discharging capacitor and the discharging current?
The same form as the charge equation.
How do you change the decay of charge equation into a log equation?
- Take logs of both sides
- Split up the logs on the right hand side
- Use the ln(e^A) = A rule to make the equation
What do you get if you plot a graph of ln(Q) against t and what is the gradient equal to?
A straight line graph. The gradient is equal to -t/RC.
What is RC?
The time constant.
What two factors does charging and discharging times depend on?
- The capacitance of the capacitor
- The resistance of the circuit
What is the time constant?
When t=RC and it is the time taken for the charge on a discharging capacitor to fall to about 37% of the original charge.
Also time taken for the charge on a charging capacitor to rise to about 63% of Q0.
How can you find the time constant using a graph?
By finding 37% (on a discharging graph) or 67% (on a charging graph) of Q0 and seeing which time it is equivalent to.
What is the time to halve?
The time taken for the charge, current or potential difference of a discharging capacitor to decrease to half of the initial value.
What is the equation for time to halve and what do the letters mean?
T1/2 = 0.69RC
R - resistance of fixed resistor
C - capacitance of the capacitor
