4.1 Capacitance

Question 1

What is a capacitor?

Answer 1

A pair of conducting plates separated by an insulator. If a potential difference is placed across the plates, they acquire equal and opposite changes.

Question 2

What is the capacitance in words?

Answer 2

It is the charge stored on the plates per unit p.d.

Question 3

What is capacitance in terms on an equation?

Answer 3

C = Q/V
Capacitance = Charge on either plate/ P.d.

Question 4

What is the formula for internal energy in a capacitor?

Answer 4

U = 1/2 QV
Internal energy = 1/2 (Charge)(Voltage)

or U = 1/2 CV² = Q²/2C

Question 5

What is the formula for capacitance using physical dimensions?

Answer 5

C = εA/d
Capacitance = permittivity of free space x Area of plates / distance between plates

ε (Permittivity of free space) = 8.85x10^-12Fm^-1

Question 6

What is the unit for capacitance?

Answer 6

Farad (F)
F = C/V = (Coulomb/ p.d.)

Question 7

What is the equation for the strength of the magnetic field between two plates of a capacitor?

Answer 7

E = V/d
Field strength = Voltage/ Distance

Question 8

What is the equation for total capacitance of capacitors in series?

Answer 8

1/Ctotal = 1/C1 + 1/C2 + 1/C3 +….

You can work it out by: Ctotal = 1/(1/C1 + 1/C2 +…)

Question 9

What is the equation for total capacitance of capacitors in parrallel?

Answer 9

Ctotal = C1 + C2 + C3 +…

Question 10

What is the equation for a discharging capacitor?

Answer 10

Q = Qoe^t/RC

Qo = original charge
R = resistance
C = capacitance
Q = Charge at time, t

Question 11

What is the equation for a charging capacitor?

Answer 11

Q = Qo(1-e^t/RC)
Qo = original charge
R = resistance
C = capacitance
Q = Charge at time, t

Question 12

What happens once a capacitor is charged?

Answer 12

The current stops flowing through it

Question 13

What is the time constant?

Answer 13

In the equation Q = Qoe^t/RC

RC is the time constant.

Question 14

What percentage of the original charge is left when time constant = t?

Answer 14

When RC = t :
Percentage left = e^-1 x100 = 37%
Therefore, 37% of the charge is left and it has decreased by 67%

Question 15

In what capacitor circuit is voltage the same across each capacitor?

Answer 15

Capacitors in parallel have the same voltage

Question 15

In what capacitor circuit is the charge the same across each capacitor?

Answer 15

Capacitors in series have the same charge across each

Question 16

What happens to the current when a capacitor is charging?

Answer 16

The current decreases at an exponentially decreasing rate.
I = Ioe^t/RC

Question 17

What happens to the charge and p.d. when a capacitor is charging?

Answer 17

They increase at an exponentially decreasing rate.
X = Xo(1- e^t/RC)

where X = Q or V

Question 18

What is the experiment for investigating the charging and discharging of a capacitor to determine the time constant?

Answer 18

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

Question 19

What is the experiment for investigating the energy stored in a capacitor?

Answer 19

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.