capacitors Flashcards
what do capacitors do
store up electrical charge
what is a capacitor made of
two conducting plates operated by a gap or dielectric
what happens when a capacitor is connected to a power source
positive and negative charge build up on opposite plates
what happens when positive and negative charge builds up on the plates of a capacitor
a uniform electric field is created between them
what is capacitance
the amount of charge per unit potential difference
capacitance equation
C = Q/V
Q is charge in coloumbs
v is potential difference in volts
capacitance in farads
what units will you see farads expressed in
uF — microfarads (× 10–6)
nF — nanofarads (× 10–9)
pF — picofarads (× 10–12
what is permittivity
Permittivity is a measure of how difficult it is to generate an electric field in a certain material.
what is the relative permittivity
The relative permittivity is the ratio of the permittivity of a material to the permittivity of free space:
what is relative permittivity known as
dielectric constant
what happens when no charge is applied to a capacitor in terms of molecules
Imagine a dielectric is made up of lots of polar molecules — they have a positive end and a negative end.
When no charge is stored by the capacitor, there is no electric field — so these molecules point in a bunch of random directions.
what happens when charge is applied to a capacitor in terms of molecules
When a charge is applied to a capacitor, an electric field is generated. The negative ends of the molecules are attracted to the positively charged plate and vice versa. This causes all of the molecules to rotate and align themselves with the electric field. The molecules each have their own electric field, which in this alignment now opposes the
applied electric field of the capacitor. The larger the permittivity, the larger this opposing field is. This reduces the overall electric field, which reduces the potential difference needed to charge the capacitor — so the capacitance increases.
how do you work out the capacitance of a capacitor using the dimensions
of the capacitor and the permittivity of the dielectric
C=Aε₀εr/d
what happens as charge builds up on the plates of a capacitor
electrical energy is stored by the capacitor
on a charge against potential difference graph for a capacitor what is the area under it
energy stored
how do you know that the charge against potential difference will be a straight line through orgin
because potential difference across a capacitor is directly proportional to the charge stored on it
if there’s a higher capacitance what is true about the energy stored
the energy stored will be higher
energy equation for capacitor
E=1/2 QV
explain how a capacitor begins charging
As soon as the switch closes, current starts to flow. The electrons flow onto the plate connected to the negative terminal of the dc power supply, so a negative charge builds up.
This build-up of negative charge repels electrons off the plate connected to the positive terminal of the power supply, making that plate positive. These electrons are attracted to the positive terminal of the power supply. An equal but opposite charge builds up on each plate, causing a potential difference between the plates. Remember that no charge can flow between the plates because they’re separated by an insulator (a vacuum, gap or dielectric). As charge builds up on the plates, electrostatic repulsion makes it harder and harder for more electrons to be deposited. When the p.d. across the capacitor is equal to the p.d. across the power supply, the current falls to zero.
how to discharge capacitor
Remove the power supply from the test circuit on and close the switch to complete the circuit. Let the capacitor discharge whilst the data logger records potential difference and current over time. When the current through the ammeter and the potential difference across the plates are zero, the capacitor is fully discharged.
the time it takes to discharge and charge depends on
1) The capacitance of the capacitor (C). This affects the amount of charge that can be transferred at a given potential difference.
2) The resistance of the circuit (R). This affects the current in the circuit.
how would you describe the the growth rate of charge or potential difference
exponential
how do you calculate the charge on the plates at a given time after a capacitor begins charging
Q=Q₀(1- e ^-t/RC)
how do you calculate the potential difference on the plates at a given time after a capacitor begins charging
V=V₀(1- e ^-t/RC)
how do you calculate the current at a given time as a capacitor is charging
I=I₀e ^-t/RC
why does it always take same length of time for the charge to halve no matter how much charge you start with
because the charge left on the plates falls exponentially with time as a capacitor discharges
how to work out the charge left on the plates as a capacitor discharges
Q=Q₀e ^-t/RC
how to work out the potential difference across the plates as a capacitor discharges
V=V₀e ^-t/RC
how to work out the current as a capacitor discharges
I=I₀e ^-t/RC
what is the time constant
the time constant, is the time taken for the charge, to fall to 37% of its value when fully charged.
or
It’s also the time taken for the charge or potential difference of a charging capacitor to rise to 63% of its value when fully charged.
what is true about the time when there is a larger resistance in series with the capacitor
the longer the it takes to discharge or discharge
what happens when you take natural log of of both sides of Q=Q₀e ^-t/RC
ln(Q) = (-1/RC)t + ln(Q₀)
what is the time to halve
time taken for the charge current or potential difference of a discharging capacitor to reach half of the value it was when it was fully charged
time to halve equation
T(1/2)=0.69RC
