# Unit 4: Section 3 - Capacitance

Notes from the A2 physics revision book

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## Capacitors

Capacitors store electrical charge.

Capacitance is defined as the amount of charge stored per volt

C = Q / V

V is the potential difference and C is capacitance in farads (F). 1 F = 1 C V^-1(coulomb per volt)

When charge builds up on the plates of a capacitor, electrical energy is stored by the capacitor. This energy can be worked out by calculating the area under a graph of potential difference(p.d) - charge stored(Q)

E = <span>½ QV = ½ base x height</span>

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## Capacitors Cont.

There are three equations for the energy stored by a capacitor:

1) E = ½ QV

2) E = ½ CV²

3) E = ½ Q² / C

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## Charging And Discharging

You can charge a capacitor by connecting it to a battery. When the capacitor is connected a current flows until the capacitor is fully charged. Electrons flow onto a plate connected to the negative terminal of the battery, therefore a negative charge builds up. This build up causes electrons to be repelled off the plate connected to the positive terminal making that plate positive. This causes a potential difference between the two plates. Since there is an insulator between the two plates no charge flows between them. While the capacitor is charging the current gradually decreases to zero as pd increases to it's maximum.

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## Charging And Discharging Cont.

A charged capacitor is connected across a resistor, the pd creates a current through the circuit. This current flows in the opposite direction to the charging current. If there is a voltmeter in the circuit, you can observe the decrease in voltage. When the p.d. across the plates is zero, the capacitor is fully discharged.

The time it takes to charge or discharge a capacitor depends on two things:

1) The capacitance of the capacitor. This affects the charge that can be transferred at a certain voltage.

2) The resistance of the circuit. This affects the current

A capacitor discharges exponentially with time. This means that no matter the charge, it takes the same length of time for the charge to halve. The graphs of V against t, and l against t for charging and discharging are also exponential

Q = Q0e ^ (- t / RC)

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## Charging And Discharging Cont.

Time constant, τ = RC

When this is put into the equation: Q = Q0e ^ (- t / RC)

You get: Q = Q0e ^ (- t / T)

So when t = τ

Q / Q0 =1 / e

Where, 1 /e ≈ 1 / 2.718 ≈ 0.37

So, τ is the time taken for the charge on a discharging capacitor to fall to 37% of Q0

It is also the time taken for the charge of a charging capacitor to rise to 63% of Q0

The larger the resistance in series with the capacitor, the longer it takes to charge or discharge. In practise, the time taken for a capacitor to fully charge or discharge is taken to be around 5RC

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Alright Sir I didn't know you had this?!

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As a Head Teacher, I believe this banter with students to be deeply inappropriate.

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GSB "L.S Steve"!

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Thank you! Though I didn't see anything on leakage current.

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Includes essential equations but you may find it easier to understand if you can also draw the graphs.  Area under the graph of voltage across a capacitor versus the charge stored = energy stored.

The same goes for charge/time and current/time graphs for discharging capacitors.  The significance of the time constant T as a point where the discharge time is equal to RC can be easily seen.

Teacher Tip: when working out the total capacitance of capacitors in series or parallel the rules are the swapped resistor rules  e.g you add together the resistors values when they are arranged in series but you add capacitor values together when they are arranged in parallel.

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