# Unit 4 Section 3 Charging and Discharging

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## Charging

• When a capacitor is connected to a D.C. power supply, a current flows in the circuit until the capacitor is fully charged, then stops.
• Electrons flow from the negative terminal of the supply onto the plate connected to it, so a negative charge builds on that plate.
• At the same time, electrons flow from the other plate to the positive terminal of the supply, making that plate positive.
• These electrons are repelled by the negative charge on the negative plate and attracted to the positive terminal of the supply.
• The same number of electrons are repelled from the positive plate as are built up on the negative plate.
• This means an equal but opposite charge builds up on each plate, causing a potential difference between the plates.
• No charge flows directly between the plates because they are seperated by an insulator(dielectric).
• Initially the current through the circuit is high.
• But as charge builds up on the plates, electrostatic repulsion makes it harder for electrons to be deposited.
• When p.d. across the capacitor is equal to the p.d. across the supply, the current falls to zero and the capacitor is fully charged.
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## Charging Through a Fixed Resistor

• As soon as the switch is closed, a current starts to flow.
• The potential difference across the capacitor is zero at first, so there is no p.d. opposing the current.
• The p.d. of the battery causes an initial relatively high current to flow, equal to V(of the supply)/R(of the resistor).
• As the capacitor charges, the p.d. across the resistor gets smaller (because the p.d. across the capacitor is getting bigger) so the current drops.
• Charge (Q) is proportional to potential difference, so the Q-t graph is the same shape as the V-t graph

I-t charging graph is a decreasing curve

V-t charging graph is an increasing curve

Q-t charging graph is an increasing curve

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## Investigating Capacitors Discharging

If you connect a voltage sensor attached to a datalogger across the capacitor, you can plot a discharge curve for the capacitor.

I-t discharge graph is a decreasing curve, V-t discharge graph is a decreasing curve, Q-t discharge graph is a decreasing curve

Q = Qo x e^-t/RC

Q = Charge of the capacitor at time t, in C

Qo = Charge when capacitor is fully charged, in C

e = (10 to the power of' whatever follows the e)

t = time since discharging began, s

R = Resistance of the fixed resistor, in Ohms

C = Capacitance of the capacitor, in F

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## Time Constant

Time constant: The time taken for the charge on a discharging capacitor to fall 1/e (about 37%) of its initial charge, or for the charge of a charging capacitor to rise to about 63% of the full charge.

When discharge time is equal to RC the equation becomes:

Q = Qo x e^-1

So when t = RC:

Q/Qo = 1/e

1/e = 1/2.718

= 0.37

The larger the resistance in series with the capacitor, the longer it takes to charge or discharge.

In practice, the time taken for a capacitor to fully charge or discharge is taken to be about 5RC or 5t

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