# Capacitors

Capacitors

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## What is Capacitance?

Definition of Capacitance

• Capacitance is defined as the amount of charge stored per volt
• C=Q/V
• Capacitance is measured in Farads(F)
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## Practicals involving Capacitors

You can investigate the Charge stored by a Capacitor Experimentally

• Set up a test circuit to measure current and potential difference
• Constantly adjust the variable resistor to keep charging current constant for as long as possible
• NB-it is impossible to keep charging current constant when capicitor is nearly fully charged
• At regualr intervals record p.d until it equals the battery p.d
• It is then possible to plot graphs of Current(I)/Amps vs Time(t)/seconds and Charge(Q)/Coulombs vs Potential Difference(V)/Volts
• Gradient of Q/p.d is Capacitance
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## Capacitance and Energy

Capacitors store Energy

• When charge builds up on plates of the capacitor, electrical energy is stored
• Area under graph of p.d vs charge stored=energy stored in the capacitor
• p.d across the capacitor is proportional to charge stored on it
• therefore the graph will be a straight line through the origin
• Area under graph(triangle) -E=1/2xQV

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## Charging a Capacitor

A capacitor can be charged by connecting it to a battery

• when connected to a battery, a current flows in circuit until  capacitor is fully charged, then stops
• Electrons flow onto negative terminal plate- (-ve) charge builds
• Build up of (-ve) charge repels electrons off plate connected to positive terminal of battery, making that plate positive
• These electrons are attracted to the positive terminal of the battery
• An equal and opposite charge builds plates. Causes Potential Difference between them (NB-no charge can flow between plates-Insulator)
• Current starts high. As more charge builds up electrostatic repulsion makes it more difficult for electrons to be deposited
• When p.d across capacitor=p.d across battery, current is 0
• Capacitor is now fully charged
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## Discharging a Capacitor

To Discharge a Capacitor, Take out the Battery and Reconnect the Current

• When a charged capacitor is connected across a resistor, the p.d drives a current through the circuit
• This current flows in opposite direction from charging current
• If a voltage sensor attached to a datalogger is connected across the capacitor , a discharge curve can be plotted
• Capacitor is fully discharged when p.d across plates and current in circuit are both zero.
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## Charging and Discharging

The Time Taken to charge or discharge depends on:

• Capacitance of Capacitor (C). This affects the amount of charge that can be transferred at a given voltage.
• Resistance of circuit (R). This affects the current in the circuit.

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## Charging and Discharging

The Charge on a Capacitor Decreases Exponentially

• When the capacitor discharges, the charge left on the plates falls exponentially with time
• Therefore it always takes the same length of time for the charge to halve, no matter how much charge you start with
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## Time Constant = RC

• Time constant, is time taken for charge on a discharging capacitor to fall to 37% of Qo
• Therefore its also time taken for charge of a charging capacitor to rise to 63% of Qo
• The larger the resistance in series with the capacitor the longer it takes to charge/discharge
• In practice, time taken for capacitor to charge/discharge fully is about 5RC
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