Capacitors in Circuits
Electricity & Electronics 8:
Capacitors in Circuits
AIM
This unit considers, in more detail, the charging and discharging of capacitors. It then
investigates how capacitors behave in ac circuits and describes some of their uses.
OBJECTIVES
On completing this unit you should be able to:
• sketch graphs of current vs time and of voltage vs time for the charge and discharge
of a capacitor in a dc circuit containing a resistor and capacitor in series.
• carry out calculations involving voltage and current in CR circuits using basic circuit
rules (V = IR and Vs = V1 + V2).
• state the relationship between current and frequency in a capacitive circuit.
• describe the principles of a method to show how the current varies with frequency in
a capacitive circuit.
• describe and explain the function of a capacitor blocking dc while passing ac.
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Electricity and Electronics
Capacitors in Circuits
ACTIVITY 11
Title: Charging and Discharging Characteristics for a Capacitor
Aim: To observe the variation of the current through, and the p.d. across, a capacitor during
the charge and discharge cycles.
Apparatus
2200 µF capacitor, 10 kΩ resistor, ammeter and voltmeter, 6 V battery
stopclock
-
V
Instructions
+
A
Part 1: Charging
• Set up the circuit as shown with the switch open. The two meters will be replaced by
connections to a computer interface.
• Close the switch and start the stopclock.
• Record values of current I and p.d. V every 10 seconds until the measured p.d. becomes
constant.
• Plot graphs of current I and p.d. V against time for the charging cycle.
• Describe the change in the current and p.d. during the charging cycle.
Part 2: Discharging
jo in
le a d s
V
+
A
•
•
•
•
Fully charge the capacitor as in Part 1.
Disconnect the leads from the battery and join them together, as shown above.
The two meters will be replaced by connections to a computer interface.
Close the switch and note values for current I and p.d. V for the capacitor every 10 seconds
from time t = 0.
• Plot graphs of current I and p.d. V against time for the discharge cycle.
• Explain the change in current and p.d. during the discharging cycle.
• Compare the direction of current during the charging and discharging cycles and explain
any differences.
Capacitance in a d.c. Circuit
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Electricity and Electronics
Capacitors in Circuits
Charging
Consider the following circuit:A
When the switch is closed the current flowing in the circuit and the voltage across the
capacitor behave as shown in the graphs below.
p.d. across
capacitor
current
Supplyvoltage
0
0
time
time
Consider the circuit at three different times.
0
0
A
As soon as the switch is
closed there is no charge on
the capacitor the current is
limited only by the
resistance in the circuit and
can be found using Ohm’s
law.
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0
A
A
+ +
+ +
+ +
-
--
-
As the capacitor charges a
p.d. develops across the
plates which opposes the
p.d. of the cell as a result
the supply current
decreases.
-3-
--
The capacitor becomes
fully charged and the p.d.
across the plates is equal
and opposite to that across
the cell and the charging
current becomes zero.
Electricity and Electronics
Capacitors in Circuits
Discharging
Consider this circuit whenthe capacitor is
fullycharged, switchtopositionB
If the cell is takenout of the circuit andthe
switchis set toA, the capacitor will
discharge
A
A
-- --
B
A
B
A
++ ++
While the capacitor is discharging the current flowing in the circuit and the voltage across
the capacitor behaves as shown in the graphs below.
p.d. across
capacitor
Current
0
Supply voltage
0
time
time
Although the current/time graph has the same shape as that during charging the currents in
each case are flowing in opposite directions. The discharging current decreases because the
p.d. across the plates decreases as charge leaves them.
Factors affecting the rate of charge/discharge of a capacitor
• When a capacitor is charged to a given voltage the time
taken depends on the value of the capacitor. The larger the
capacitor the longer the charging time, since a larger
capacitor requires more charge to raise it to the same p.d.
as a smaller capacitor as V= Q
C
• When a capacitor is charged to a given voltage the time
taken depends on the value of the resistance in the circuit.
The larger the resistance the smaller the initial charging
current, hence the longer it takes to charge the capacitor
as Q = It
(The area under this I/t graph = charge. Both curves will
have the same area since Q is the same for both.)
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C u rre n t
la rg e c a p a c ito r
s m a ll c a p a c ito r
T im e
C u rre n t
s m a ll re s is to r
la rg e re s is to r
T im e
Electricity and Electronics
Capacitors in Circuits
Example
The switch in the following circuit is closed at time t = 0
10 V
Vs
1 M
1 µF
Immediately after closing the switch what is:
(a)
the charge on C
(b)
the p.d. across C
(c)
the p.d. across R
(d)
the current through R.
When the capacitor is fully charged what is:
(e)
the p.d. across the capacitor
(f)
the charge stored.
(a)
(b)
(c)
(d)
(e)
(f)
Initial charge on capacitor is zero.
Initial p.d . is zero since charge is zero.
p.d. is 10 V = Vs - Vc = 10 - 0 = 10 V
I
10
= V =
= 10 3 A
R
10 6
Final p.d. across the capacitor equals the supply voltage = 10 V.
Q = CV = 2 × 10-6 × 10 = 2 × 10-5 C.
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Electricity and Electronics
Capacitors in Circuits
Frequency response of capacitor
The following circuit is used to investigate the relationship between current and frequency in
a capacitive circuit.
A
C u rren t
(A )
S ig n a l
gen erato r
(co n stan t
e .m .f.)
0
freq u en cy (H z )
The results show that the current is directly proportional to the frequency of the supply.
To understand the relationship between the current and frequency consider the two halves of
the a.c. cycle.
Electrons
-
+
+
Electrons
The electrons move back and forth around the circuit passing through the lamp and charging
the capacitor one way and then the other (the electrons do not pass through the capacitor).
The higher the frequency the less time there is for charge to build up on the plates of the
capacitor and oppose further charges from flowing in the circuit More charge is transferred in
one second so the current is larger.
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Electricity and Electronics
Capacitors in Circuits
Blocking DC
2 V DC
(a) dc supply
The lamp does not light.
2.5 V
Lamp
1000 µF
capacitor
Current flows only while the capacitor charges. In this circuit, this takes a matter of
milliseconds! This short burst of current is not sufficient to light the lamp. When the capacitor
is charged, the current in the lamp is zero so it does not light
2 V AC
(b) ac supply (50 Hz)
The lamp lights continuously.
2.5 V
Lamp
1000 µF
capacitor
The alternating supply voltage pushes current one way then quickly reverses and pushes it the
opposite way. Current flows on and off the plates of the capacitor continuously, causing an
alternating current in the lamp which therefore lights.
Learning point: A capacitor blocks dc but can allow ac to flow in a circuit.
Use of capacitor to block dc while passing ac
Blocking capacitors are used to connect the different stages of amplification in a power
amplifier. They are so called because they allow the ac (audio) signals to flow from one stage
of amplification to the next while blocking the dc voltages which are present in the preceding
stage. These dc voltages must not be amplified or they would ultimately be large enough to
destroy the loudspeaker connected to the output stage.
Technicians examining ac signals in an item of electronic equipment often find that the ac
trace is thrown off the top of the CRO screen by the presence of a large dc voltage in the
circuit. By pushing in the “ac” switch on the front of the CRO, a capacitor is placed in series
with the input. This capacitor blocks the dc voltage leaving the ac signal displayed
conveniently in the centre of the screen.
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Electricity and Electronics
Capacitors in Circuits
Applications of Capacitors (for background interest)
Blocking capacitor
A capacitor will stop the flow of a steady d.c. current . This is made use of in the a.c./d.c.
switch in an oscilloscope. In the a.c. position a series capacitor is switched in allowing
passage of a.c. components of the signal, but blocking any steady d.c. signals.
Flashing indicators
A low value capacitor is charged through a
resistor until it acquires sufficient voltage to
fire a neon lamp. The neon lamp lights when
the p.d. reaches 100 V. The capacitor is
quickly discharged and the lamp goes out
when the p.d. falls below 80V.
1 - 2 M
120 V
Crossover networks in loudspeakers
In a typical crossover network in low cost
loudspeaker systems, the high frequencies are
routed to LS-2 by the capacitor.
LS 1
LS 2
Smoothing
The capacitor in this simple rectifier circuit is storing charge during the half cycle that the
diode conducts. This charge is given up during the half cycle that the diode does not conduct.
This helps to smooth out the waveform.
I
C a p a c ito r
c h a rg e s
C a p a c ito r
d is c h a r g e s
t
Capacitor as a transducer
A parallel plate capacitor can be used to convert mechanical movements or vibration of one of
its plates into changes in voltage. This idea forms the basis of many measuring systems, e.g.
by allowing a force to compress the plates we have a pressure transducer.
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Electricity and Electronics
Capacitors in Circuits
ACTIVITY 13
Title: Current and frequency in a capacitive circuit
Aim:
To find how changing the frequency of the ac supply affects
the current flowing in a circuit containing a capacitor.
Apparatus: Signal generator (Unilab 062.101)
Digital ammeter (200 mA ac)
Analogue voltmeter (10 V ac)
Capacitor (100 microfarad; non-polar)
Five connecting leads
Circuit:
A
Initial set up:
•
•
•
•
•
V
Connect the Lo output of the signal generator in series with the ammeter and
capacitor using three of the connecting leads.
Connect the voltmeter in parallel with the capacitor using the remaining two
leads.
Set the range switch on the signal generator to x 10 Hz.
Set the frequency control to 11 to give a frequency of 110 Hz.
Using the amplitude control, set a voltage across the capacitor that results in an
ammeter reading close to, but not exceeding, 200 mA.
You must ensure, by adjustment if necessary, that this voltage remains the same for the rest
of the experiment.
Obtaining results:
•
•
•
•
Note the setting of the frequency control.
Note the size of the current flowing in the circuit.
Continue by setting lower frequencies on the signal generator.
Use an appropriate format to show the relationship between the current and the
frequency in a circuit containing a capacitor.
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Electricity and Electronics
Capacitors in Circuits
Capacitors in Circuits
15.
The circuit below is used to investigate the charging of a capacitor.
A
10 kΩ
12 V
2000 µF
(a)
(b)
(c)
(d)
16.
What is the response of the ammeter when switch S is closed?
How can you tell when the capacitor is fully charged?
What would be a suitable range for the ammeter?
If the 10 kΩ resistor is replaced by a larger resistor, what will be the effect on
the maximum voltage across the capacitor?
In the circuit below the neon lamp flashes at regular intervals. The neon lamp requires
a potential difference of 100 V across it before it will conduct and flash. It continues
to glow until the potential difference across it drops to 80 V. While lit, its resistance is
very small compared with R.
R
120 V dc
(i)
(ii)
C
Explain why the neon bulb flashes.
Suggest two methods of decreasing the flash rate.
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Electricity and Electronics
Capacitors in Circuits
18.
The circuit below is used to charge and discharge the capacitor
1
VR
2
100 V
VC
(a)
(b)
(c)
What position should the switch be set (i) to charge and (ii) to discharge the
capacitor?
Draw graphs of VR against time for the capacitor charging and discharging, and
of VC against time for the capacitor charging and discharging.
If the capacitor has capacitance of 4.0 µF and the resistor has resistance of 2.5
MΩ calculate:
(i)
the maximum charging current in the circuit above
(ii)
the maximum charge stored by the capacitor when fully charged in the
above circuit.
19.
3 MΩ
3V
3 µF
(a)
(b)
20.
For the above circuit draw graphs of
(i) VC against time during charging and
(ii) VA against time during charging.
Calculate the final voltage across the capacitor and the final charged stored by
it.
For each of the circuits below state what happens to the current flowing when the
frequency is (i) increased and (ii) decreased.
L o w v o lt a g e
v a r ia b le
freq u en cy
s u p p ly
C ir c u it 1
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C ir c u it 2
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Electricity and Electronics
Capacitors in Circuits
21.
In the circuit below the signal generator is set at 6.0 Vr.m.s., 1000 Hz.
The lamp operates normally.
S ig n a l
gen erato r
(a)
(b)
22.
Explain why the lamp can operate normally when the plates of the capacitor
are separated by an insulator.
What happens to the brightness of the lamp when the frequency of the signal
generator is increased. Why does this happen?
For each of the following circuits sketch a graph of current against frequency.
A
A
S ig n a l
g e n e ra to r
D ia g ra m A
D ia g ra m B
23.
A
B
S ig n a l
g e n e ra to r
The supply frequency to the above circuit is increased from a very low frequency,
while the supply voltage remains constant.
What will happen to the brightness of lamp A and B?
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Electricity and Electronics