Capacitors

Question 1

Define Capacitance ?

Answer 1

the capacitance of an object is the amount of charge that is able to store per unit potential difference across it
C = Q/V
- measured in F or CV^-1
- Capacitance of a capacitor is charge on one plate

Question 2

Relationship between charge and potential difference ?

Answer 2

the charge of a capacitor is proportional to the potential difference across it
Q∝V (CV = Q) - Capacitance is a constant

Question 3

What does the charge/potential difference graph look like ?

Answer 3

• straight line through the origin
• gradient is the capacitance
• area under graph is the energy stored
  E = 1/2QV = 1/2CV^2 = 1/2 Q^2/C

Question 4

How energy stored by capacitor ?

Answer 4

charges on the plates are being forced together but want to repel so this requires energy.
E ∝ V^2

Question 5

What does Dielectrics and relative permittivity (Er) mean ?

Answer 5

Dielectrics are insulators
- Permittivity is a measure of how difficult it is to generate an electric field in a medium.
- different material have different RELATIVE PERMITTIVITY - Dielectric constant
- increase the Permittivity = more charge needed to produce an electric field.
Er = E1/Eo

Question 6

Describe the rotations of particles in a dielectric material when charge is stored on a capacitor ?

Answer 6

when there is a E-field present then the molecules to align anti-parallel to the electric field
- the molecules produce own E-field which opposes the applied E-field of capacitor
- this reduces the resultant electric field + potential difference
- capacitance increases (C=Q/V)
C = AErEo/d
(A = surface area of one plate )

Question 7

How charge is built up on the plates of a capacitor ?

Answer 7

1) electrons flow from negative terminal to plate which causes negative build up
2) electrons flow opposite way from other plate to positive terminal which causes a positive build up
3) equal but opposite charge build up on each plate which causes a potential difference

Question 8

How voltage, charge and current vary with time as a capacitor charges ?

Answer 8

VOLTAGE
- increases EXPONENTIALLY with time at capacitor
- decreases EXPONENTIALLY with time at resistor
- Vc + Vr = Vt
CHARGE
- increases EXPONENTIALLY with time at capacitor
CURRENT (rate of flow of electrons)
- decreases EXPONENTIALLY with time at capacitor

Question 9

Calculations with charging capacitor ?

Answer 9

• Q = Qo(1-e^-t/RC)
• V = Vo(1-e^-t/RC)
• I = Ioe^-t/RC

Question 10

How charge is discharged on the plates of a capacitor ?

Answer 10

1) take out battery + reconnect the circuit
2) with a resistor is a circuit a current flow through circuit in opposite way to charging current
3) it fully discharged when potential difference across plates and current across circuit is zero

Question 11

Calculations with Dis-charging capacitor ?

Answer 11

• Q = Qoe^-t/RC
• V = Voe^-t/RC
• I = Ioe^-t/RC
  All decrease exponentially with time

Question 12

How to plot log-linear graph for Dis-charging capacitor ?

Answer 12

e.g. Q = Qoe^-t/RC
ln(Q) = (-1/RC)t + ln(Qo)
y = mx + c 
- gradient = -1/RC
- Y-intercept = ln(Qo)
Helps to produce a straight line instead of a curve

Question 13

What is the time constant ?

Answer 13

is the time taken for a discharging capacitor to discharge to 1/e (37%) of its initial charge
T = RC
(time constant = resistance x capacitance)
- measured in ΩF

Question 14

What is the time to halve ?

Answer 14

is the time taken for charge/p.d/current of a discharging capacitor to fall to half if its initial value
T1/2 = 0.69RC

Question 15

How to determine the time constant from graphs ?

Answer 15

on CHARGING graph -> read value corresponding to = 0.63Qo
on DISCHARGING graph -> read value corresponding to = 0.37Qo
- resistance or capacitance increases = T increases