- 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.
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
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
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
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