A2/A-level Physics - Capacitance

Capacitance (C ) is charged stored per unit p.d. (voltage). It is measured in farads (F), where 1F = 1 Q V^-1. Capacitance is created by capacitors, they are:

• Two metal plates, place close together, so they can ‘experience’ one and others ‘activity’, without touching
• This is joined to a circuit, with a cell/ battery
• The cell or battery, push electrons from the negative terminal to the neutral plate (relatively positive) of the capacitor (notice electron flow without complete circuit)
• electrons build up in the plate
• the plate becomes more negatives, so less electron are attracted
• The negativity is ‘experienced’ by the other plate which pushes a few more electrons on that place
• This makes one plate negative and the other positive, hence a p.d of the cell is created between the two plates (capacitors)

As charge (Q) builds up (electors), the voltage(V) builds up proportionally (as each electron are pushed by the same cell with same energy), hence the proportionality constant is given by capacitance(C).

The overall capacitance for a circuit with multiple capacitors is given by:

Series- is the sum of the inverse of each capacitor, because the current in each capacitor is the same but the voltage is different. As:

• V=Q/C
• Q_T=Q₁=Q₂=Q₃
• V_T = V₁+V₂+V₃  ➔  Q/C_T = Q/C₁+ Q/C₂+ Q/C₃ (divide both side by Q)

Parallel- is the sum of each capacitors, because the voltage stays the same on different junctions but current changes. As a result:

• Q=VC
• V_T=V₁=V₂=V₃
• Q_T = Q₁+Q₂+Q₃  ➔  VC_T= VC₁+VC₂+VC₃  (divide both side by V)

The energy stored in a capacitor is given by the area under the graph. This is because V=W/Q, and the total energy stored is sum of all energy held by all charges (i.e. the area of the graph). This gives us the formula for work (energy), which can also be manipulated by substituting Q=CV,if we have an unknown.

In A2/A-level Physics, drawing graphs will help your understanding! 👨‍🏫

As time increases in a:

Charging capacitor:

• Current decreases exponentially (goes less positive, as it is less attractive)
• Charge increases, with the rate of increase, decreasing with time (plateaus)
• Voltage increases, with the rate of increase, decreasing with time (plateaus)

Discharging capacitor:

• Current increases (goes less negative), with the rate of increase, decreasing with time (plateaus)
• Charge decreases exponentially
• Voltage decreases exponentially

Time constant is the inverse coefficient of exponential discharge of a capacitor each time, given by the product of resistance (R) of a circuit and capacitance (C). The amount of discharge has a

Constant-ratio property, hence:

• t=nT ➔ x= x₀e^-n

The uses of capacitors include storage of energy in applications such as:

• flash photography
• lasers used in nuclear fusion
• back-up power supplies for computers

Reference:

https://getrevising.co.uk/resources/capacitance_ocr_unit_5_module_2

This is the end of the topic! Well done!

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