# Capacitors

• Created by: emma
• Created on: 14-05-13 18:36

## Investigating charge stored on a capacitor

• set up test circuit with battery, variable resistor, ammetre, voltmetre, switch and capacitor.
• adjust variable resistor in order to keep charging current constant.
• record pd at regular intervals until it equals battery pd.
• plot a current-time graph. the area under this is the charge stored on the plates.
•  plot a charge time graph ( Q = IT). the gradient of this equals capacitance.
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## Charging a capacitor

• capacitor is connected to a battery
• current flows in circuit until capacitor is fully charged, then stops.
• electrons flow to plate connected to negative terminal
• this repels charge from other plate (connected to + terminal)
• initialy, current through circuit is high
• charge builds up
• electrostatic repulsion makes it harder for charge to be deposited
• pd across capacitor = pd across battery, current falls to 0
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## Discharging a capacitor

• Either take out battery or reconnect circuit
• pd drives current through circuit
• current flows in opposite direction to charging current
• pd across plates and current = 0
• capacitor = fully discharged

charge decreases exponentially with time (it always takes the same amount of time for charge to halve)

graphs of q, i or v against t for charging and discharging are exponential.

Time taken to charge or discharge depends on:

• capacitance
• resistance
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## Time constant

Time constant, t = time taken for charge on discharging capacitor to fall to 37% of its original value.

it's also the time for a charging capacitor to rise to 63% of Qo

the larger the resistance in series wuth the capacitor, the longer it takes to charge.

5RC is time for capacitor to fully discharge.

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## Energy stored by a capacitor

• work done when charge,q moves through pd, v, = w=vq

but...

• pd varies as capacitor charges
• v and q are proportional
• average pd = half of final pd
• v against q graph - area equals the work done in charging the capacitor
• the capacitor stores the transferred energy as electric potential energy.
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