Chapter 21 - Capacitors Flashcards
what is a capacitor
- a capacitor is an electrical component which separates charge
- it’s formed of 2 metallic plates separated by an insulator
how is a capacitor charged
- when a capacitor is connected to a cell (emf, E) electrons flow from the cell to the capacitor but cannot pass between the plates
- this causes electrons and a negative charge to build up on one of the plates
- this negative charge induces an equal and opposite charge on the opposite plate as like charges repel
- this creates a p.d. across the plates of the capacitor
- the current in the circuit stops flowing and the capacitor stops charging when the p.d. across the plates is equal to the emf of the cell
define capacitance
“the capacitance of a capacitor is the ratio of charge stored by the capacitor to the potential difference across it”
what is the key equation for capacitors
Q = VC charge = voltage x capacitance
what is the farad
the farad is the unit of capacitance equaivalent to 1 coulomb per volt
what is the equation for total capacitance from 2 or more capacitors in parallel
Ctot = C1 + C2 + C3…
how to derive the capacitance in parallel equation
- in parallel, V is constant
- charge is conserved so Qtot = Q1+ Q2…
- so using Q = VC
VtotCtot = V1C1 + V2C2 … - all V values are the same so
- Ctot = C1 + C2 etc.
what are the three things to remember about capacitors in a parallel circuit
Qtot = Q1 + Q2 …
Ctot = C1 + C2 …
V is constant
what is the equation for capacitance in a series circuit
1/Ctot = 1/C1 + 1/C2 …
how to derive the equation for capacitance in series
in series charge is constant but voltage is shared, as V = Q/C
we have Vtot = V1 + V2 …
gives
Qtot/Ctot = Q1/C1 + Q2/C2 …
the Q’s cancel as they are all equal giving
1/Ctot = 1/C1 + 1/C2 …
what are the three things to remember about capacitors in series circuits
1/Ctot = 1/C1 + 1/C2 …
Vtot = V1 + V2 …
charge is constant
describe the practical for capacitance combinations
- set up a variety of circuits
- set multimeter to capacitance
- place across each capacitor individually, measure capacitance
- measure overall capacitance by placing across the combinations
- compare to calculated values
in actual terms what is the work done by/on a capacitor which causes there to be an energy storage and what does the work
work must be done to cause a charge on each plate:
- it requires energy to ‘push’ a negative electron towards a negative plate
- it also requires work to remove an electron from the opposite plate
- work is done by the cell
what represents the energy stored by a capacitor
- the area under a p.d. - charge graph
- this gives the equation
W = 1/2 QV
what are the variations of the capacitor energy equation
W = 1/2 QV gives
W = 1/2 V^2 C w = 1/2 Q^2/C
what is the standard circuit used for charging/discharging a capacitor
a cell connected in parallel with a capacitor and a resistor but there’s a switch which can flick from connecting capacitor and cell to capacitor and resistor
at T=0 what is the p.d. across the capacitor and resistor (at instant switch is closed), what is the initial current in the resistor and the initial charge on the capacitor
where the cell had emf Vo
P.d. across capacitor/resistor = Vo
current in resistor = Vo/R
charge on capacitor = VoC
what is the generalised equation for discharging a capacitor
X = X0 e^-t/RC
what happens to voltage, charge, and current in relation to the capacitor when discharging
they all undergo exponential decay
define the time constant and what is the equation for the time constant
“the time constant, T (tau), for a discharging capacitor is equal to the time taken for the p.d. across the capacitor to drop to e^-1 or about 37% of its initial value”
tau = RC
what happens when charging capacitors in terms of the variables, V, Q, and I
V and Q increase reverse exponentially sort of thing, I decreases exponentially
what is the generalised equation for the exponential growth of V and Q when charging a capacitor
X = Xo (1-e^(-t/RC))
what is the equation for current when charging a capacitor
the same as when discharging a capacitor
I = Io e^(-t/RC)
what are the main features of capacitors mean they can be useful
- they are compact
- cannot store a lot of energy in a small volume but can release their energy very quickly
- this quick release of energy can give them a large output power
what are 2 common uses of capacitors
- emergency lighting (large time constant)
- camera flashes
what is the circuit used for smoothing capacitors
input voltage –> diode –> resistor in parallel –> capacitor in parallel –> output voltage
what is the purpose of this smoothing capacitor circuit
- it converts the input voltage which is AC to a DC output voltage
how does this smoothing circuit work
- the diode prevents one direction of current from passing giving bits of voltage in only one direction
- the capacitors allow current to still flow in one direction even when the diode is preventing the opposite direction from passing
- for this to be effective it must be tau»_space; period
if the current in the charging circuit is kept constant, what is the graph for voltage over the capacitor against time and why
- a straight line with positive gradient because V = Q/C V = IT/C so if I is constant and C is constant then V = (I/C) T as a y = mx+c graph
why are the charges on opposite plates of a capacitor equal and opposite
- the same number of electrons are deposited/ removed from the opposite plates
what is the gradient of a ln(V) against t graph and what is the Y-intercept
gradient = -1/tau y-int = ln(Vo)
if you have two capacitors connected in parallel but no power source i.e. one/both of the capacitors is charged but maybe differently, how can you calculate the final voltage on them
- charge is conserved, they are in parallel
- calculate total charge on the charged capacitors
- voltage must be constant in parallel hence
V = Q/C
so calculate total capacitance and do total charge/ total capacitance = voltage on both
