C21 - Capacitance Flashcards
What are capacitors?
Electrical components which separate charge.
It consists of 2 metallic plates separated from each other by an insulator (often dielectric e.g. air, paper, ceramic etc).
What happens when a capacitor is connected to a cell of emf, ℰ?
Electrons flow from the cell for a short time.
They cannot travel between the capacitor plates because of the insulation.
This brief current means electrons are removed from plate A of the capacitor and the same time electrons are deposited into plate B.
A becomes electron deficient and has a net + charge, B gains electrons and has a - charge.
They have equal and opposite charges, Q. Net charge on the capacitor is 0.
What’s capacitance?
C = Q/V
Charge stored per unit p.d. across it.
What is capacitance, C, measured in?
Farads, F
What happens (to p.d., charge and capacitance) when capacitors are connected in parallel?
The p.d. across each capacitor is the same
Electrical charge is conserved therefore total charge stored is equal to sum of individual charges (Q = Q1 + Q2…)
Total capacitance is the sum of individual capacitances of the capacitors (C = C1 + C2…)
What happens (to p.d., charge and capacitance) when capacitors are connected in series?
According to Kirchhoff’s second law, the total p.d. across the combination is the sum of the individual p.d.s across the capacitors (V = V1 + V2…)
The charge Q stored by each capacitor is the same
Total capacitance C is given by the equation 1/C = 1/C1 + 1/C2…)
What does a potential difference - charge graph look like?
What are features of the graph?
Charge Q along x axis
Potential difference V along y axis
Straight line through origin
Gradient = 1/capacitance
Area under graph is equal to work done
How do current I₀, voltage V₀ and charge Q₀ change over time as a capacitor discharges?
They all have the same shape and show exponential decay (demonstrate a half life).
What’s time constant, τ?
The product of capacitance and resistance, CR, for a capacitor-resistor circuit.
This is equal to the time taken for the p.d., current or charge to decrease to 1/e of its original value when the capacitor discharges through a resistor.
How can the equation “ ΔQ/Δt = -Q/CR “ be used to model the decay of charge on a capacitor (via iterative modelling)?
1) Start with a known value for the initial charge (Q₀) and time constant (CR).
2) Choose a time interval which is very small compared to the time constant.
3) Calculate the charge leaving the capacitor in a time interval using: ΔQ = Δt/CR * Q
4) Calculate the charge left on the capacitor at the end of the period Δt by subtracting ΔQ from the previous charge.
5) Repeat for subsequent multiples of the time interval Δt.
How are capacitors discharged?
(For a circuit with a capacitor and a resistor with a voltmeter connected in parallel to a battery).
When the switch is opened, the capacitor discharges through the resistor.
The charge stored by the capacitor decreases with time and hence the p.d. across it also decreases.
Current in the resistor decreases with time as the p.d. across it decreases accordingly.
Eventually, the p.d., charge and current in the resistor will all be zero.
How are capacitors charges?
(For a circuit with a capacitor, resistor and switch in series with a battery).
When the switch is closed, there’s a maximum current in the circuit and the capacitor begins to charge.
The p.d. across the capacitor starts to increase from 0 as it gathers charge.
According to Kirchoff’s second law, the p.d. across the resistor V(R) across the resistor and p.d. across the capacitor V(C) must always add up to V(0).
Therefore V(R) must decrease as V(C) increases with time.
After a long time, depending on time constant, the capacitor will be fully charged with a p.d. of V(0), and V(R) will be zero.
How does current and p.d. in a circuit decrease over time?
Exponentially
x=xe^-(t/CR)
Where x = I
What rules must be considered when analysing circuits where a capacitor is charged through a resistor?
- V, I and R are related by V = IR
- V, Q and C are related by Q = VC
- Current in the circuit is given by the equation I = I(0) e^ − (t/CR)
- The equation x = x0 (1-e ^(-t/CR)) may be used for the capacitor, where x can be either charge on the capacitor or p.d. across the capacitor
- At any time t, the p.d. across the components add up to V(0).
V(0) = V(R) + V(C)
How much energy can capacitors store?
They’re compact and can easily be charged.
Unlike chemical cells, they can’t store much energy and release it very quickly.
