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Module 6 - Chapter 21 - Capacitance II - Coggle Diagram
Module 6 - Chapter 21 - Capacitance II
Discharging capacitors
Exponential decay - quantities decreasing by the same factor in equal time intervals
Opening switch
Pd across capacitor/ resistor =
Current in the resistor is
In the capacitor, the charge stored is
Process
Capacitor discharges through resistor, the charge decreases wtih time and so does the pd across it
Disconnect the power supply and connect a resistor
When power is no longer connected, electrons on negative plate aren't held in place by the emf, so repel
Initiall, the pd across the plates is at a maximum
Flowing electrons decreases stored charge and pd decreases over capacitor so current decreases
This continues until no charge is stored on the capacitor
Equations
Modelling
Capacitor and resistor in parallel have the same pd
For a capacitor,
, the charge on the capacitor decreases with time
therefore,
Iterative modelling
Start with a known value for Initial charge and known time constant
Choose time intervale which is very small compared with time constant
Calculate the charge leaving the capactitor using the equation
Calculate the charge remaining on the capactiro at the end by subtracting the change in charge from initial charge
Repeat for subsequent multiple of time interval
Logarithms
Plot lnV on y axis and t on the x gives a gradeitn of -1/CR
lnVnought is the y intercept
Time constant
Lower resistance means higher current, and charge on plate falls to zero faster
It equals the time taken for the pd/charge/current to decrease to 37% of its initial value
A farad ohm is the same as a second
The product CR (time constant) in exponential decay has the same unit as time
Charging capacitors
Charging
Closing the switch leads to a maximum current in the circuit and capacitor starts to charge up
Pd across capacitor increases from zero as it gathers charge
Vr and Vc must add up to V0, so Vr must decreases as Vc increases
When the capacitor is fully charged, it has a pd of V0, so Vr is 0, and the current in the circuit is 0
Equations
Since V=IR, the pd across resistor Vr decreases exponentially with respect to time
Uses
Power
Capacitors can't store large amounts of energy in a small volume
Capacitors can release stored energy very quickly, and generate high output power
Smoothing capacitors
Domestic electricity is supplied as AC
Capacitors can be used to change ac into a smooth direct voltage
Dioide allows current in one direction only, and without the capacitor, output voltage from the circuit would only be positive
Using a capacitor, output voltage is smoothed out and becomes almost direct voltage
To reduce ripples in output voltage, time constant can be kept much greater than the period of alternating voltage (T)
Ripples
Diode allows the capacitor to charge up
As soon as the input voltage decreases, the capacitor starts to discharge through the resistor
Vripple is the difference between the maximum and minimum output voltage
for small ripples, t is approximately T
, e^-x = 1-x when x is small
Dimensions
Capacitance depends on the number of electrons that can be stored on the negative plate,a so is directly proportional to the area of the plates
Attraction between charges on plates depends on plate separation,d so capacitance is indirectly proportional to d
With a vacuum, capacitance is
For non vacuum insuilators, permittivity is
, where er is relative permittivity
