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Physics Year 13 > Chapter 21 - Capacitors > Flashcards

Chapter 21 - Capacitors Flashcards

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1
Q

what is a capacitor

A
  • a capacitor is an electrical component which separates charge
  • it’s formed of 2 metallic plates separated by an insulator
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2
Q

how is a capacitor charged

A
  • 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
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3
Q

define capacitance

A

“the capacitance of a capacitor is the ratio of charge stored by the capacitor to the potential difference across it”

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4
Q

what is the key equation for capacitors

A 
Q = VC
charge = voltage x capacitance
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5
Q

what is the farad

A

the farad is the unit of capacitance equaivalent to 1 coulomb per volt

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6
Q

what is the equation for total capacitance from 2 or more capacitors in parallel

A

Ctot = C1 + C2 + C3…

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7
Q

how to derive the capacitance in parallel equation

A
  • 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.
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8
Q

what are the three things to remember about capacitors in a parallel circuit

A

Qtot = Q1 + Q2 …
Ctot = C1 + C2 …
V is constant

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9
Q

what is the equation for capacitance in a series circuit

A

1/Ctot = 1/C1 + 1/C2 …

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10
Q

how to derive the equation for capacitance in series

A

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 …

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11
Q

what are the three things to remember about capacitors in series circuits

A

1/Ctot = 1/C1 + 1/C2 …
Vtot = V1 + V2 …
charge is constant

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12
Q

describe the practical for capacitance combinations

A
  • 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
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13
Q

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

A

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
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14
Q

what represents the energy stored by a capacitor

A
  • the area under a p.d. - charge graph
  • this gives the equation
    W = 1/2 QV
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15
Q

what are the variations of the capacitor energy equation

A

W = 1/2 QV gives

W = 1/2 V^2 C
w = 1/2 Q^2/C
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16
Q

what is the standard circuit used for charging/discharging a capacitor

A

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

17
Q

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

A

where the cell had emf Vo
P.d. across capacitor/resistor = Vo
current in resistor = Vo/R
charge on capacitor = VoC

18
Q

what is the generalised equation for discharging a capacitor

A

X = X0 e^-t/RC

19
Q

what happens to voltage, charge, and current in relation to the capacitor when discharging

A

they all undergo exponential decay

20
Q

define the time constant and what is the equation for the time constant

A

“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

21
Q

what happens when charging capacitors in terms of the variables, V, Q, and I

A

V and Q increase reverse exponentially sort of thing, I decreases exponentially

22
Q

what is the generalised equation for the exponential growth of V and Q when charging a capacitor

A

X = Xo (1-e^(-t/RC))

23
Q

what is the equation for current when charging a capacitor

A

the same as when discharging a capacitor

I = Io e^(-t/RC)

24
Q

what are the main features of capacitors mean they can be useful

A
  • 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
25
Q

what are 2 common uses of capacitors

A
  • emergency lighting (large time constant)

- camera flashes

26
Q

what is the circuit used for smoothing capacitors

A

input voltage –> diode –> resistor in parallel –> capacitor in parallel –> output voltage

27
Q

what is the purpose of this smoothing capacitor circuit

A
  • it converts the input voltage which is AC to a DC output voltage
28
Q

how does this smoothing circuit work

A
  • 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&raquo_space; period
29
Q

if the current in the charging circuit is kept constant, what is the graph for voltage over the capacitor against time and why

A 
- 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
30
Q

why are the charges on opposite plates of a capacitor equal and opposite

A
  • the same number of electrons are deposited/ removed from the opposite plates
31
Q

what is the gradient of a ln(V) against t graph and what is the Y-intercept

A 
gradient = -1/tau
y-int = ln(Vo)
32
Q

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

A
  • 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

Physics Year 13 (15 decks)

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