Capacitors Flashcards
What is the capacitance of an object?
The amount of charge it is able to store per unit potential difference across it
What is capacitance measured in?
Farads
What is 1 Farard equal to?
1 coulomb per volt
What is the equation for capacitance?
C = Q/V
C: Capacitance
Q: Charge
V: Potential difference
What is a capacitor?
An electrical component that can store electrical charge
What are capacitors made of?
2 electrical conducting plates separated by an electrical insulator
What is the circuit symbol of a capacitor?
2 parallel lines pointing vertically (—-| |—-)
Describe what happens when a capacitor is connected to a DC power source
Charge builds up on its plates, with one becoming negatively charged and the other becoming positively charged
Why are the 2 plates in a capacitor separated by an electrical insulator?
So no charge can move between the plates, meaning a potential difference builds up between the plates
What is the voltage rating of a capacitor?
The maximum potential difference you can safely put across it
What is 1nF (nanofarad) equal to?
10^-9 farads
What is 1μF (microfarad) equal to?
10^-6 farads
What is 1pF (picofarad) equal to?
10^-12 farads
How do you experimentally investigate the relationship between the potential difference across a capacitor, and the amount of charge it stores?
Set up a circuit including a power source, switch, capacitor, variable resistor, ammeter and voltmeter. Close the switch and constantly adjust the variable resistor to try and keep the charging current constant. Measure the p.d. at regular intervals until it equals the battery p.d. Then plot a graph of current against time
Describe for a current (μA)-time graph looks like for a capacitor
A square where the corner furthest away from the origin is the point at which the capacitor is fully charged
Why is the current (μA)-time graph for a capacitor a square?
Because once the capacitor is fully charged, the current drops to zero
What is the area under a current (μA)-time graph for a capacitor equal to?
Charge stored on plates
Describe the proportionality between Q and V for a capacitor
Q and V are directly proportional
Why are capacitors not used instead of batteries?
Because they can only store a small amount of charge
What are capacitors used for?
To provide power for a short amount of time
Why are capacitors very dangerous?
Because they store charge and then can discharge it all in a fraction of a second, enough charge to kill you
Give 2 examples of where capacitors are used
Camera flash
To smooth out variations in DC voltage supplies
Why are capacitors used in camera flash?
The battery in the camera charges the capacitor over a few seconds, then the entire charge is dumped into the flash almost instantly producing a very bright light for a short amount of time
What happens inside a capacitor as it charges?
One plate becomes negatively charged and the other becomes positively charged. Like charges repel, so energy is needed to force the charges on the plate together. This energy is stored as electric potential energy and is supplied by the power source
What happens inside a capacitor when the charges are released?
Not as much energy is needed to force the charges together, so electric potential energy is released
What is the equation for the energy stored in a capacitor?
E = 0.5QV
E: Energy stored
Q: Charge on capacitor
V: Potential difference across capacitor
How can you derive the equation for the energy stored in a capacitor?
It’s the area under a V-Q (or Q-V) graph for a capacitor. As V is directly proportional to Q for the capacitor, the graph is a straight line through the origin, meaning the area under the graph is a triangle. 0.5 x base x height = 0.5QV
How is the energy stored by a capacitor related to the energy supplied by the power source?
Energy stored by capacitor is half energy supplied by power source
Why is only half of the energy supplied by a power source stored in a capacitor?
The other half is lost to resistance in the circuit and internal resistance of the battery
What is the equation for the energy stored by a capacitor when you’re given the potential difference and capacitance?
E = 0.5CV^2
E: Energy stored
C: Capacitance
V: Potential difference across capacitor
What is the equation for the energy stored by a capacitor when you’re given the charge and capacitance?
E = 0.5 (Q^2 / C)
E: Energy stored
Q: Charge
C: Capacitance
What is permittivity?
A measure of how difficult it is to create an electric filed in that material
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?
A ratio of the permittivity of a material to the permittivity of free space
What is the equation for relative permittivity?
εr = ε1 / ε0
εr: Relative permittivity
ε1: Permittivity of material 1
ε0: Permittivity of free space
What is the other name given to relative permittivity?
Dielectric constant
What is the name of a capacitor made from parallel plates separated by a dielectric?
Parallel-plate capacitor
What is a parallel-plate capacitor?
A capacitor made from parallel plates separated by a dielectric
How can you describe permittivity?
A dielectric has lots of polar molecules. When the 2 parallel plates become charged, all the polar molecules rotate so that the positive end is attracted to the negative plate and vice versa. Each molecule now has its own electric field, which opposes the applied electric field of the capacitor. The larger the permittivity, the larger this opposing field is, which reduces the overall electric field between the plates, thus increasing the capacitance
What is the second equation for capacitance, if you know the dimensions of the capacitor?
C = (A ε0 εr) / d
C: Capacitance A: Effective area of plate ε0: Permittivity of free space εr: Relative permittivity d: Distance between capacitor plates
How does increasing the distance between the plates in a capacitor affect capacitance?
Capacitance decreases
How does increasing the relative permittivity of the dielectric affect the capacitance?
Capacitance increases
How does increasing the area of the plates affect the capacitance?
Capacitance increases
How can you investigate capacitance?
Set up 2 parallel plates with a dielectric, then connect the plates to a capacitance meter. Change variables such as distance between plates to see the effect on the capacitance
What happens when a capacitor is connected to a DC power supply?
A current flows in the circuit until the capacitor is fully charged, at which point it stops
How does a capacitor charge?
Electrons flow from the negative terminal of the power supply onto the connected plates, making it negatively charged. Electrons from the other plates flow to the positive terminal of power supply making that plate positive. The same number of electrons are repelled from the positive plate as are built up on negative plate, causing an equal but opposite charge, meaning a potential difference
When a circuit that charges a capacitor is switched on, why does the current start high but decrease?
As charge builds up on the plates, electrostatic repulsion makes it harder for more electrons to be deposited. When the p.d. across the capacitor equals the p.d. across the supply, the capacitor is fully charged
What happens to the current of a circuit when a capacitor is fully charged?
It drops suddenly to zero
When charging a capacitor through a fixed resistor, what affect does the resistance of the resistor have on the circuit?
It affects the time taken to charge the capacitor
What is the area under a current-time graph equal to?
Charge stored
What is the equation for the charge of a charging capacitor after a given time?
Q = Q0(1 - e^-(t/RC))
Q: Charge of capacitor at time t Q0: Charge of capacitor when fully charged t: Time since charging begun R: Resistance of fixed resistor C: Capacitance
What is the equation for the voltage across a charging capacitor after a given time?
V = V0(1 - e^-(t/RC))
V: p.d. of capacitor at time t V0: p.d. of capacitor when fully charged t: Time since charging begun R: Resistance of fixed resistor C: Capacitance
What is the equation for the current of a charging capacitor after a given time?
I = I0 e^-(t/RC)
I: Current of capacitor at time t I0: Initial current t: Time since charging begun R: Resistance of fixed resistor C: Capacitance
Describe what happens when charging a capacitor through a fixed resistor
When current starts to flow, the p.d. across the capacitor is zero, so no p.d. opposing current. As the capacitor starts charging, the p.d. across the capacitor gets bigger, the p.d. across the resistor gets smaller, and the current drops
When is a capacitor fully discharged?
When the p.d. across the plates and the current in the circuit are both zero
How do you discharge a capacitor?
Disconnect the power source and reconnect the circuit
What is the equation for the charge of a discharging capacitor after a given time?
Q = Q0 e^-(t/RC))
Q: Charge of capacitor at time t Q0: Charge of capacitor when fully charged t: Time since charging begun R: Resistance of fixed resistor C: Capacitance
What is the equation for the voltage of a discharging capacitor after a given time?
V = V0 e^-(t/RC))
V: p.d. of capacitor at time t V0: p.d. of capacitor when fully charged t: Time since charging begun R: Resistance of fixed resistor C: Capacitance
What is the equation for the current of a discharging capacitor after a given time?
I = I0 e^-(t/RC)
I: Current of capacitor at time t I0: Initial current t: Time since charging begun R: Resistance of fixed resistor C: Capacitance
What is a log-linear plot?
A graph where one of the axes is logarithmic
Why do we use log-linear and log-log plots?
Because often they produce a straight line graph, whereas linear axes would be a curve
When you plot a graph of charge of capacitor when fully charged against time since discharging, what should the axes be to produce a straight line
X-axis is t and Y-axis is ln(Q0)
log-linear graph
When plotting ln(Q0) against t, how do you find the time constant?
By diving -1 by the gradient
What 2 factors affect the time taken for a capacitor to charge or discharge?
- The capacitance of the capacitor
- The resistance of the circuit
When the t=RC, what is the equation for charge of a discharging capacitor then equal to?
Q = Q0 e^-1
How does the equation Q = Q0 e^-1 link to the time constant?
Rearrange to get Q/Q0 = 1/e
1/e = 0.37 = 37%
What is the time constant?
Time taken for the charge on a discharging capacitor to fall to about 37% of what Q0, or time taken for the charge of a charging capacitor to rise to about 63% of Q0
The larger the resistance in series with the capacitor, the…?
Longer it takes to charge or discharge
What is the symbol for time constant?
Tau (τ)
Seen as Q is proportional to V, what is the time constant also equal to?
Time taken for the voltage on a discharging capacitor to fall to about 37% of the source voltage, or time taken for the voltage of a charging capacitor to rise to about 63% of source voltage whilst charging
What is the equation for time constant?
τ = RC
τ: Time constant
R: Resistance of fixed resistor
C: Capacitance of capacitor
How can you find time constant from a graph?
Work out what 37% of Q0 (if discharging) or 63% of Q0 (if charging), then find where it intersects the Q0-t graph
What is the time taken for a capacitor to fully charge or discharge roughly equal to?
5RC = 5τ
What is the time to halve of a capacitor?
The time taken for the charge, p.d. or current of a discharging capacitor to decrease to half its initial value
Q = 0.5 Q0
What is the equation for the time to halve?
T1/2 = 0.69RC
T1/2: Time to halve
R: Resistance of fixed resistor
C: Capacitance of capacitor
In the equation for time to halve, where does the number 0.69 come from?
Because Q = 1/2 Q0, you can cancel out and substitute to get:
1/2 = e^(-t/RC) which then rearrange to get t = ln(2)RC
ln(2) = 0.693
How can you find the time to halve from a graph of charge, p.d. or current?
Read off the value of t which corresponds to half the initial value of charge, current or p.d.
