Capacitors

Question 1

State the structure of a capacitor

Answer 1

Conductor | insulator | conductor

Most commonly, they are two metal plates separated by a material called a dielectric

Question 2

What is the function of a capacitor?

Answer 2

To store charge

Question 3

Explain what happens when a capacitor is connected to a source of emf

Answer 3

• a current flows
• charge is stored on the two plates (+Q and -Q)
• when the pd across the plates equals the emf of the cell, the current stops
• the total charge on the capacitor is zero

Question 4

Define and state the equation for capacitance

Answer 4

The value of Q per volt across the capacitor is called capacitance

capacitance = charge stored/pd
C = Q/V

Question 5

State three useful properties of supercapacitors

Answer 5

• can have a capacitance >1000F
• not chemical like cells
• do not degrade over time

Question 6

How do you calculate total capacitance for capacitors in parallel?

Answer 6

C total = C1 + C2 + C3 etc

Question 7

How do you calculate total capacitance for capacitors in series?

Answer 7

1/C total = 1/C1 + 1/C2 + 1/C3 etc

Question 8

State the properties of a graph of pd vs charge for a charging capacitor

Answer 8

• a straight line graph through the origin
• gradient = 1/C
• the total work done in storing all the charge is the area under the graph

Question 9

State three equations for calculating energy stored by a capacitor

Answer 9

W = 1/2QV
W = 1/2CV²
W = 1/2 x Q²/C

Question 10

What is the time constant in a capacitor discharge equation

Answer 10

time constant = RC

Question 11

What are the 3 exponential decay equations for capacitor discharge?

Answer 11

Q = Q₀e^-t/RC
V = V₀e^-t/RC
I = I₀e^-t/RC

Question 12

Define time constant

Answer 12

The time it takes for Q, V or I to fall to 0.37 of its original value

For every equal step along the x-axis, the y-axis should fall by the same fraction

Question 13

How does current vary with time when a capacitor is charging?

Answer 13

The current will initially be high, and will fall off exponentially - this is the same as for discharging

Question 14

State the 3 equations for a charging capacitor

Answer 14

x = x₀(1 - e^-t/RC)
Q = Q₀(1 - e^-t/RC)
V = V₀(1 - e^-t/RC)

Question 15

State two uses of capacitors

Answer 15

• camera flash
• smoothing signals when turning A.C to D.C

Question 16

For a parallel plate capacitor, what is the relationship between its capacitance (C), the area of overlap of the two plates (A) and the separation of the plates (d)

Answer 16

C ∝ A/d

Question 17

State the constant added to the relationship between C, A and d, and the equation it produces

Answer 17

Constant = permittivity (ε)
And ε = ε0 x εr
So, C = ε0εrA/d

Question 18

Derive an equation for capacitance for an isolated sphere

Answer 18

V = Q/4πε0r and Q = CV
V = CV/4πε0r
1 = C/4πε0r
C = 4πε0r