Download Charge, Voltage and Capacitance

Charge, Voltage and Capacitance
Electricity & Electronics 6:
Charge, Voltage and Capacitance
AIM
In this unit you are going to investigate capacitors. You may have already met them in the
Electronics unit of Standard Grade Physics, where one was used to introduce a delay into a
circuit – useful in burglar alarms. Capacitors are used in many electrical circuits including
flash guns, microphones, graphic equalisers, amplifiers, televisions, videos and computers.
OBJECTIVES
On completing this unit you should be able to:
• state that the charge on two parallel conducting plates is directly proportional to the
potential difference between them.
• describe the principles of a method to show that the pd across a capacitor is
proportional to the charge on the plates.
• state that capacitance is the ratio of charge to pd (i.e. charge per unit volt)
• state that the unit of capacitance is the farad and that one farad is one coulomb per
volt
• carry out calculations using C = Q/V .
• describe and explain the function of a capacitor used for storing charge.
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Electricity and Electronics
Charge, Voltage and Capacitance
Capacitance
The ability of a component to store charge is known as capacitance.
A device designed to store charge is called a capacitor.
A typical capacitor consists of two conducting layers separated by an insulator. These layers
are then often rolled into a cylindrical shape.
Relationship between charge and p.d.
A
+
B
C
V
-
The capacitor is charged to a chosen voltage by
setting the switch to A. The charge stored can be
measured directly by discharging through the
coulomb meter with the switch set to B. In this way
pairs of readings of voltage and charge are obtained.
Q
Charge is directly proportional to voltage.
0
Q
= constant
V
V
For any capacitor the ratio Q/V is a constant and is called the capacitance.
farad (F)
capacitance =
charge
voltage
coulombs (C)
volts (V)
The farad is too large a unit for practical purposes.
In practice the micro farad (µF) = 1 × 10-6 F and the nano farad (nF) = 1 × 10-9 F are used.
Example
A capacitor stores 4 × 10-4 C of charge when the potential difference across it is 100 V.
What is the capacitance ?
Q
C =
=
V
4 × 10 100
6
= 4 µF
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Electricity and Electronics
Charge, Voltage and Capacitance
DC Power Supply - Using a capacitor to store charge
Many power supplies deliver dc to the appliance they are connected to (any electronic device, for
example - phone charger, computer power supply, and so on). They have to convert the ac of the
mains to dc. (Note that a transformer is used to drop the 230 V ac mains to the required voltage before
the ac to dc conversion).
The 150 Ω resistor in the circuit represents the appliance and is known as the load resistor. The CRO
shows what is happening to the voltage over the load resistor.
Set up each circuit as shown and sketch the output waveforms on the axes provided.
1. Basic circuit - ac
12 V
voltage
150 Ω
time
CRO
2. Diode added - ‘lumpy’ dc (no negative half cycle)
voltage
12 V
150 Ω
time
CRO
3. Capacitor added - smoothing takes place
voltage
12 V
150 Ω
time
100 µF
CRO
4. Higher value capacitor added - more smoothing
voltage
12 V
150 Ω
time
1000 µF
CRO
THE CAPACITOR STORES CHARGE DURING THE WORKING HALF CYCLE.
IT DELIVERS IT TO THE LOAD DURING THE MISSING HALF CYCLE.
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-3-
Electricity and Electronics
Charge, Voltage and Capacitance
ACTIVITY 10
Title: Charge and potential difference for a capacitor
Apparatus:
(Outcome 3)
Electrolytic capacitor (about 5000 µF), coulomb meter, voltmeter, 6 × 1.5 V
battery, changeover switch
A
B
V
Coulomb meter
Instructions
• Discharge the capacitor by shorting with connecting lead.
• Connect the circuit and set the switch to charge the capacitor as shown in the diagram.
Allow enough time for the capacitor to charge fully.
• Set the switch to B to fully discharge the capacitor through the coulomb meter.
• Repeat for other charging voltages.
• Use an appropriate format to show the relationship between charge and voltage.
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Electricity and Electronics
Charge, Voltage and Capacitance
Capacitance
7.
A 50 µF capacitor is charged till the voltage across its plates reaches 100 V.
(a)
(b)
How much charge has been transferred from one plate to the other?
If it was discharged in 4 milliseconds, what would be the average current?
8.
A capacitor holds a charge of 3 × 10-4 C when it is charged to 600 V.
What is the value of the capacitor?
9.
A 30 µF capacitor holds a charge of 12 × 10-4 C.
(a)
What is the voltage that it is charged to?
(b)
If the tolerance of the capacitor is ± 5 µF, express this uncertainty as a
percentage.
(c)
What is the greatest voltage which could occur across the plates of the
capacitor?
10.
A 15 µF capacitor is charged from a 1.5 V battery. What charge will be stored on the
plates?
11.
(a)
(b)
12.
A capacitor has a voltage of 12 V across its plates and stores a charge of
1.2 × 10-5 C. Calculate its capacitance.
A 0.1 µF capacitor is connected to a 8 volt direct supply. How much charge
will it store?
Using the circuit below a capacitor is charged with a constant current of 2.0x10-5 A.
A
The time taken to charge the capacitor is 30 s and during this time the voltage across
the capacitor rises from 0 V to 12 V.
What is the capacitance of the capacitor?
17.
In the circuit below the capacitor C is charged with a steady current of 1mA by
carefully adjusting the variable resistor R.
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Electricity and Electronics
Charge, Voltage and Capacitance
A
9 Vdc
V
C
The voltmeter reading is taken every 10 seconds. The results are shown in the table.
(a)
(b)
(c)
Time
0
10
20
30
40
p.d.(V)
0
1.9
4
6.2
8.1
Plot a graph of charge against voltage for the capacitor and hence find its
capacitance (use graph paper).
Calculate the capacitance for each of the readings (ignoring readings for t = 0).
Calculate the mean capacitance and the approximate random uncertainty in the
mean to two decimal places.
Strathaven Academy
-6-
Electricity and Electronics