6 Capacitance Flashcards
capacitors
electrical components in which charge is separated.
consists of two metallic plates separated from each other by an insulator, often known as dielectric, such as air, paper, ceramic or mica
how do capacitors store charge?
when a capacitor is connected to a cell, electrons flow from the cell for a very short time. they cannot travel between the plates because of the insulator.
the very brief current means electrons are removed from plate A of the capacitor and at the same time elecs are deposited onto the other plate B
plate A becomes deficient in elecs (pos charge).
plate B gains elecs (neg charge)
the current in the circuit must be the same at all points and charge must be conserved, so the two plates have an equal but opposite charge of magnitude Q
so there is a pd across the plates
the current falls to zero when the pd is equal to the emf of the cell
the capacitor is then fully charged
the net charge on the plates is zero
capacitance
charge stored per unit pd across it C=Q/V C is capacitance in farads F Q is charge stored V is pd across the capacitor
capacitors in parallel
-pd across each capacitor is the same
-electrical charge is conserved. so the total charge stored is equal to the sum of the individual charges
Q=Q1 + Q2 +…
-the total capacitance is the sum of the individual capacitances of the capacitors
C=C1 + C2 + …
capacitors in series
-according to Kirchhoff’s second law, the total pd across the combination is the sum of the individual pds across the capacitors
V= V1 + V2 +…
-the charge stored by each capacitor is the same
-the total capacitance is given by the equation
1/C = 1/C1 + 1/C2 + …
investigating circuits
layout- an ammeter, resistor of 100 ohms, two capacitors (voltmeters in parallel) and a switch all connected in series to a power supply
when switch is closed, ammeter briefly registers a current but very quickly settles down to zero reading.
this shows that elecs move in the circuit only until the capacitors are fully charged
charges Q1 and Q2 stored by the capacitors are calculated, they should be the same. any difference is caused by the uncertainties in the voltmeter readings
technique to confirm the capacitance rules for a series circuit
multimeter set to capacitance or farads is used to determine the individual capacitance of each capacitor and then to determine the total capacitance by placing it across the combination of capacitors
pushing and removing electrons
electron moving towards the neg plate of a capacitor will experience a repulsive electrostatic force from all the elecs already on the plate
external work has to be done to push this elec onto the neg plate
work has to be done to cause an elec to leave the pos plate
the external work is provided by the battery or power supply
potential difference-charge graphs
area under pd-charge graph = work done
the work done on the charges is the same as the energy stored in the capacitor
discharging a capacitor
when switch is opened at time t=0
the pd across the capacitor or resistor= V0
for the resistor, I=V0/R
for the capacitor, charge stored Q=V0C
the capacitor then discharges through the resistor. the charge stored by the capacitor decreases with time and hence the pd across it also decreases
the current in the resistor dec with time as the pd across it dec accordingly
eventually the pd, charge stored by capacitor and current in resistor are all zero
constant-ratio property of exponential decay
graph of pd across the capacitor against time shows the characteristic shape of exponential decay with its constant-ratio property
V1/V0=V2/V1=V3/V2
time constant
equal to the product product of capacitance and resistance
a measure of how long the exponential decay will take in a particular capacitor-resistor circuit
rearrange equation for time
t= ln(X/X0) x CR
modelling exponential decay
ΔQ/t = -Q/CR
- start with known initial charge Q0 value and known time constant CR value
- choose a time interval Δt which is very small compared with the time constant
- calculate the charge leaving the capacitor ΔQ in a time interval
- calculate the charge Q left on the capacitor at the ned of the period Δt by subtracting ΔQ from the previous charge
- repeat the whole process for the subsequent multiples of the time interval Δt
charging a capacitor
when the switch is closed, there is a max current in the circuit and the capacitor starts to charge up
the pd across the capacitor starts to inc from zero as it gathers charge
according to kirchhoffs second law, the pd across the resistor and the pd across the capacitor must always add up to V0
so VR must dec as VC inc with time
after a long time, depending on the time constant CR of the circuit, the capacitor will be fully charged with a pd of V0 and VR will be zero
when this happens the current is zero
