6.1 Capacitors

Question 1

what is a capacitor?

Answer 1

a capacitor is a circuit component that stores energy by separating charges onto two electrical conductors (often called plates) with an insulator between them, one plate becomes positively charged and the other becomes negatively charged

Question 2

what is the name of the insulating material between the plates of a capacitor?

Answer 2

dielectric

Question 3

what is the circuit symbol for a capacitor?

Answer 3

two parallel lines connected with wires either side

Question 4

how does a capacitor charge up? what happens to the voltage across the capacitor and the current when the capacitor is fully charged?

Answer 4

• when a capacitor is connected to a source of emf such as a cell, charge cannot flow between the plates of the capacitor
• electrons will be transferred from the negative terminal onto one plate, which becomes negatively charged and off the other plate, which becomes positively charged
• this results in a potential difference across he plates of the capacitor
• once the capacitor has become fully charged, no more charge will flow in the circuit, since the electrons on the negatively charged plate will repel any further electrons away
• at this point, the potential difference across the capacitor will be equal to the emf of the cell, there will also be no current

Question 5

what is the definition of capacitance?

Answer 5

the capacitance, C, of a capacitor is defined as the quantity of charge. Q, which can be stored per unit p.d, V. across the plates of the capacitor

Question 6

what is the definition of capacitance?

Answer 6

the capacitance, C, of a capacitor is defined as the quantity of charge. Q, which can be stored per unit p.d, V, across the plates of the capacitor

Question 7

what is the unit of capacitance?

Answer 7

farads, F

Question 8

why do we not use farads when stating the capacitance of capacitors?

Answer 8

a farad is a huge unit, so usually capacitance is usually expressed as micro-farads, more appropriate unit

Question 9

what is the rule for combining capacitance in parallel?

Answer 9

Ct = C1 +C2 +C3
because voltage across all capacitors is the same as the cell and and the charge adds up to total
(opposite to resistors same as springs)

Question 10

what is the rule for combining capacitance in series?

Answer 10

1 / Ct = 1 / C1 + 1 / C2 + 1 / C3
because every plate has the same magnitude of charge and the voltage adds up to total
(opposite to resistors same as springs)

Question 11

what does the area under a voltage-charge graph represent?

Answer 11

the energy stored by the capacitor, or the work done by the battery to separate the charges on the two plates

Question 12

what are the three equations for energy stored by a capacitor?

Answer 12

E = 0.5 x QV (from graph)
E = 0.5 x CV^2 (from subbing Q = CV)
E = 0.5 x Q^2 / C (from subbing in V = Q / C)

Question 13

what are some common uses of capacitors?

Answer 13

-flash photography
-backup power supplies
-smoothing out p.d
(page 136)

Question 14

what are the three exponential equations for charging a capacitor?

Answer 14

Q = Qf (1-e^-t/RC)
V = Vf (1-e^-t/RC)
I = Io x e^-t/RC

Question 15

what are the three exponential equations for discharging a capacitor?

Answer 15

Q = Qo x e^-t/RC
V = Vo x e^-t/R
I = Io x e^-t/RC

Question 16

what does the graph look like for charge against time for a capacitor charging up?

Answer 16

charge starts at 0 and gradually increases upwards exponentially until it plateaus where charge = Qf (final charge)

Question 17

what does the graph look like for voltage against time for a capacitor charging up?

Answer 17

voltage starts at 0 and gradually increases upwards exponentially until it plateaus where voltage = Vf (final voltage)

Question 18

what does the graph look like for current against time for a capacitor charging up?

Answer 18

current starts at initial current, decreases exponentially downwards until plateaus

Question 19

what does the graph look like for charge against time for a capacitor discharging?

Answer 19

charge starts at initial charge (max charge if you like) the gradually decreases exponentially downwards

Question 20

what does the graph look like for voltage against time for a capacitor discharging?

Answer 20

voltage starts at initial voltage (max voltage if you like) the gradually decreases exponentially downwards

Question 21

what is the time constant, T (tau), dependent on? and what is the equation for the time constant?

Answer 21

• the capacitance of the capacitor (C), this affects the amount of charge that can be transferred at a given voltage
• the resistance of the circuit (R). this affects the current in the circuit

T = CR

Question 22

what is the definition for the time constant (in words)?

Answer 22

the time constant, T, is the time taken fro the charge remaining on a capacitor to decrease to a 1 / e (about 37%) of its initial value, measured in seconds

Question 23

outline an experiment to investigate the way p.d and current changes as a capacitor charges and discharges

Answer 23

(see page 137 for clear diagram)

• set up a circuit with a capacitor and a voltmeter across it, connect an ammeter in series also and a resistor, use a switch with two positions to create two separates circuits, one with the cell and one with the bulb
• close the switch to position 1 to allow the capacitor to charge up, record the current and p.d values every 15 seconds or use a data logger
• then connect the switch to position 2 and monitor the current and p.d ad the capacitor discharges through the lamp
• then plot graphs of how current flowing into the capacitor and the voltage across the capacitor vary as it charges and discharges

Question 24

how does the rate of charging/discharging change?

Answer 24

discharging: the more charge on the plates, the faster they can discharge, as more charge is transferred. discharge become slower due to electron repulsion
charging: the less charge on the plates, the faster they can charge up (initial charging at the start is when it is more fast), as the capacitor gets charged up, charging becomes slower because of electron repulsion