4.1 Capacitance Flashcards
What is a capacitor?
A pair of conducting plates separated by an insulator. If a potential difference is placed across the plates, they acquire equal and opposite changes.
What is the capacitance in words?
It is the charge stored on the plates per unit p.d.
What is capacitance in terms on an equation?
C = Q/V
Capacitance = Charge on either plate/ P.d.
What is the formula for internal energy in a capacitor?
U = 1/2 QV
Internal energy = 1/2 (Charge)(Voltage)
or U = 1/2 CV² = Q²/2C
What is the formula for capacitance using physical dimensions?
C = εA/d
Capacitance = permittivity of free space x Area of plates / distance between plates
ε (Permittivity of free space) = 8.85x10^-12Fm^-1
What is the unit for capacitance?
Farad (F)
F = C/V = (Coulomb/ p.d.)
What is the equation for the strength of the magnetic field between two plates of a capacitor?
E = V/d
Field strength = Voltage/ Distance
What is the equation for total capacitance of capacitors in series?
1/Ctotal = 1/C1 + 1/C2 + 1/C3 +….
You can work it out by: Ctotal = 1/(1/C1 + 1/C2 +…)
What is the equation for total capacitance of capacitors in parrallel?
Ctotal = C1 + C2 + C3 +…
What is the equation for a discharging capacitor?
Q = Qoe^t/RC
Qo = original charge
R = resistance
C = capacitance
Q = Charge at time, t
What is the equation for a charging capacitor?
Q = Qo(1-e^t/RC)
Qo = original charge
R = resistance
C = capacitance
Q = Charge at time, t
What happens once a capacitor is charged?
The current stops flowing through it
What is the time constant?
In the equation Q = Qoe^t/RC
RC is the time constant.
What percentage of the original charge is left when time constant = t?
When RC = t :
Percentage left = e^-1 x100 = 37%
Therefore, 37% of the charge is left and it has decreased by 67%
In what capacitor circuit is voltage the same across each capacitor?
Capacitors in parallel have the same voltage
In what capacitor circuit is the charge the same across each capacitor?
Capacitors in series have the same charge across each
What happens to the current when a capacitor is charging?
The current decreases at an exponentially decreasing rate.
I = Ioe^t/RC
What happens to the charge and p.d. when a capacitor is charging?
They increase at an exponentially decreasing rate.
X = Xo(1- e^t/RC)
where X = Q or V
What is the experiment for investigating the charging and discharging of a capacitor to determine the time constant?
Equipment:
Switch, Voltmeter, Power supply, capacitor with known capacitance, resistor with known resistance.
1) Connect the circuit so there are two loops connected with a switch. One loop has the the capacitor with the voltmeter in parallel and the other with the resistor
2) Charge the capacitor (we know its charged when the voltmeter reading is constant) and record the voltage over the capacitor Vo
3) Change the switch to the resistor circuit and start the stop watch measuring the voltage across the capacitor every 10s
4) V = (Vo)e^t/RC so ln(V) = ln(Vo) - t/RC
5) Plot a graph of ln(V) (y-axis) against t (x-axis) and the straight line gradient will give -1/RC and the y intercept should be ln(Vo)
6) Rearrange to get RC = -1/Gradient where RC is the time constant
What is the experiment for investigating the energy stored in a capacitor?
Equipment- Joule meter, Variable power supply, voltmeter, two known resistors r and R, capacitor, switch.
1) Set a circuit a circuit with two loops connected with a switch. One loop has the variable power supply with the voltmeter parallel to it, resistor r and capacitor and the other has the resistor R with a joulemeter in parallel
2) Set power supply to a low pd and charge the capacitor through r with switch in upper position
3) Change the switch to discharge the capacitor until the joulemeter has settled down (stopped ticking up) and measure the reading
4) Repeat 2 or 3 times this pd
5) Repeat steps 2, 3 and 4 for different pd’s
6) Plot a graph of Energy(U) against V ² ( U = 1/2 CV²) and the gradient will be 1/2 C.
