Chapter 21 - Capacitance

Question 1

How does a battery compare to a capacitor?

Answer 1

Battery stores chemical potential, capacitor stores electrostatic
Battery continuous transfer, capacitor one time quick transfer
Both are sources of energy that transfer energy to a circuit

Question 2

What is a capacitor?

Answer 2

Device designed to store energy by storing charge in electrostatic fields in the form of potential energy

Question 3

What is the formula for capacitance?

Answer 3

C = Q / V

Question 4

What is the charged stored in a capacitor dependant on?

Answer 4

Directly proportional to surface area of plates
Inversely proportional to separation of plates
Dependant upon permittivity between plates

Question 5

What is the formula to show factors influencing capacitance?

Answer 5

C = A * E / d
= Surface Area * Permittivity of Dielectric / Distance

Question 6

What are the properties of capacitors in series?

Answer 6

Total PD is V_T = V₁ + V₂ + …
Charge on each capacitor is the same
Total capacitance is 1 / C_T = 1 / C₁ + 1 / C₂ + …

Question 7

What are the properties of capacitors in parallel?

Answer 7

PD across each capacitor is the same
Total charge is Q_T = Q₁ + Q₂ + …
Total capacitance is C_T = C₁ + C₂ + …

Question 8

What is the formula for energy stored by a capacitor?

Answer 8

E = 1/2 * Q * V
E = 1/2 * C * V²
E = 1/2 * Q² * 1/C
Area under the graph PD against Charge

Question 9

What is a resistor-capacitor circuit?

Answer 9

A circuit in which a capacitor is charged/discharged through a fixed resistor

Question 10

What is the relationship between current and time in a RC circuit?

Answer 10

Current will decrease as an exponential function w.r.t time

Question 11

What happens as more charge arrives at capacitor in RC circuit w.r.t time?

Answer 11

As more and more charge arrives at the capacitor, PD between cell and capacitor decreases, current decreases, and the rate of charging decreases

Question 12

What is the formula for current against time when charging?

Answer 12

I = I₀ * e ^-t/RC

Question 13

What is the difference between across capacitor and PD across a resistor?

Answer 13

PD across capacitor increases exponentially in time during charging and decreases during discharging
PD across resistor decreases exponentially in time whether charging or discharging

Question 14

What is the formula for PD against time for a capacitor when charging?

Answer 14

PD across capacitor increases exponentially in time

V = V₀ * (1 - e^-t/RC)

Question 15

What is the formula for PD against time across a resistor when charging?

Answer 15

PD across resistor (rest of the circuit) decreases exponentially over time

V = V₀ * e^-t/RC

Question 16

What is the relationship between charge stored by a capacitor and time when charging? Formula?

Answer 16

Charged stored by capacitor increases exponentially in time when charging
Q = Q₀ * (1 - e^-t/RC)

Question 17

What is the formula for current against time in a capacitor during discharging?

Answer 17

Current decreases exponentially in time

I = I₀ * e^-t/RC

Question 18

What is the formula for PD on the capacitor against time during discharging of the capacitor?

Answer 18

PD across capacitor decreases exponentially in time

V = V₀ * e^-t/RC

Question 19

What is the formula for PD on the resistor against time when discharging a capacitor?

Answer 19

PD across the resistor decreases exponentially in time

V = V₀ * e^-t/RC

Question 20

What is the formula for charge against time when discharging a capacitor?

Answer 20

Charged stored by capacitor decreases exponentially in time

Q = Q₀ * e^-t/RC

Question 21

What property of capacitors make them useful?

Answer 21

Capacitors discharge their energy in a very short time, giving rise to a large power output
So they can be used for large power devices as a backup power supply

Question 22

What is rectification?

Answer 22

The process of turning AC current into DC current

Question 23

What does a rectifier circuit do?

Answer 23

It coverts the half cycles of an AC signal into an unbroken series of half pulses which run in the same direction

Question 24

Why can a diode not be used on its own to rectify AC current?

Answer 24

The diode allows current to flow in one direction and so loses the negative half cycles

Question 25

What happens when a capacitor is used to rectify AC current?

Answer 25

The capacitor charges during rectifier peaks and discharges when rectifier output drops, filling in gaps in the waveform The PD is smoothed out and becomes DC current of almost constant value with ripples at the positive peaks and gradual declines in the negative

Question 26

How can the ripples produced by capacitor rectification of AC currents be reduced?

Answer 26

The ripple can be smoothed out by ensuring the circuit time constant is much greater than period of PD

Question 27

What is the method to investigate the charging of a capacitor?

Answer 27

Voltmeter over capacitor with resistor, switch, and ammeter Close switch to charge capacitor, and record voltage for time interval Plot voltage against time Plot current against time Area under I-t graph is charge in capacitor

Question 28

What is the method to investigate the discharging of a capacitor?

Answer 28

Put voltmeter in parallel with resistor and capacitor with switch between capacitor and source Allow capacitor to fully charge Start stopwatch when switch is turned and record V every time interval Graph log(V) against t m = -1/RC c = log(V₀)