Download Transformers and transmission

Transformers and transmission
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1.
Chapter
3
Identify rms voltage as an AC voltage which produces the same power in
a resistive component as a DC voltage of the same magnitude;
Convert between rms, peak and peak to peak values of voltage and current;
Analyse transformer action, modelled in terms of electromagnetic induction for an
ideal transformer, N1/N2 = V1/V2 = I2/I1;
Analyse the supply of power as P = VI and transmission losses using potential
difference across transmission lines (V = IR) and power loss (P = I2R);
Explain the use of transformers in an electricity distribution system;
Identify and apply safe and responsible practices when working with electricity and
electrical measurement.
[2 marks]
(2001 Q3)
It is common practice for the wires in the cables associated with garden lights to carry only lowvoltages (often 12 VRMS). However it is more efficient to use 240-volt globes in the lights. In
order to achieve this, the circuit shown below is used. At the 240-V supply, the voltage is
stepped down using a 240-V to 12-V transformer, and at the light it is stepped up using a 12-V
to 240-V transformer. The wires joining the two transformers are each many metres long. The
transformers can be assumed to be ideal.
The light globe is rated at 120 W when connected to a 240-VRMS supply. What current should
flow through it under this condition?
2.
[3 marks]
(2001 Q4)
When the system was tested, it was clear that the globe was not operating at the rated 120 W.
Explain the reason for this.
3.
[2 marks]
(2001 Q5)
When the garden light is operating, the voltage across the input to the transformer that supplies
the globe is 10 VRMS. What is the voltage across the globe?
4.
[2 marks]
(2001 Q6)
Under these conditions the current flowing through the long wires is 8.3 A.
What current is flowing through the globe?
5.
[2 marks]
(2001 Q7)
What is the total resistance of the two wires? Remember that the transformers are ideal.
6.
[2 marks]
(2001 Q8)
Which one or more of the following changes would increase the voltage across the globe?
A. use wires of higher resistance
B. use wires of lower resistance
C. use transformers with ratios of 240:24 and 24:240
D. use transformers with ratios of 240:6 and 6:240
7.
[2 marks]
(2001 Q12)
A portable electric heater has two settings, ‘high’ and ‘low’. These heating levels are obtained
by connecting two heating elements either in series or in parallel, across the 240-VRMS mains
supply. Each element has the same electrical resistance.
When the heating elements are connected in series, the total power dissipated in them is 960 W.
What is the resistance of each element?
8.
[2 marks]
What is the value of the ratio
9.
[3 marks]
(2001 Q13)
total power dissipated in heating elements in series
?
total power dissipated in heating elements in parallel
(2002 Q1)
The 60-watt light bulb in Sam’s desk lamp has burnt out. There is no spare replacement that
operates on the 240-V supply. However, a 60-watt light bulb is found that operates at 120 V.
Sam suggests building the following circuit in order to use the 120-V light bulb.
What is the value of the resistor R that will allow the 120-V light bulb to operate correctly?
10.
[3 marks]
(2002 Q2)
The Smith family and the Jones family are farmers near Warragul. Their electricity supply
comes more than 100 km, from a power station in the LaTrobe Valley. It is carried by
transmission lines, at a voltage of 220 kVRMS.
Near the town, a switchyard-transformer (T1) steps the voltage down to 10 kVRMS for the local
area. A 10-kVRMS line runs to the Jones’ farm, where there is a transformer (T2) that provides 240
VRMS for the farms.
A 240-VRMS line then runs 2 km to the Smith’s farm. A sketch of the situation is shown below.
The transformers can be considered to be ideal.
Explain why the supply from the power station to the local area is chosen to be 220 kVRMS rather
than at 240 VRMS.
Use numerical estimates to support your answer.
11.
[1 mark]
(2002 Q3)
Assume that the input voltage to transformer T1 is 220 kVRMS, and the output is 10 kVRMS.
What is the value of the ratio:
number of turns on the primary coil
?
number of turns on the secondary coil
12.
[3 marks]
(2002 Q4)
The supply and the return lines between transformer T2 and the Smith’s farm have a total
resistance of 0.0004 ohm m-1.
At a particular time, 20 A of current is being supplied to the Smith’s farm. Assume that the
potential at the secondary for transformer T2 is 240 VRMS.
What is the voltage at the Smith’s farm?
13.
[2 marks]
(2002 Q5)
Sometimes strings of Christmas-tree lights consist of three groups of globes that are connected
as shown below
There are 16 globes in group P. Each of the globes has a voltage of 10 V across it and a current of
0.50 A flowing through it when the string of lights is operating as designed. The globes in
groups Q and R have a different power rating to those in group P.
The number of globes in groups Q and R is equal. Although they have a different power rating
from the globes in group P, the potential difference across each globe is still 10 V when
operating.
How many globes are there in group Q?
14.
[2 marks]
(2002 Q6)
What current is being supplied from the electricity supply to the string of lights?
15.
[3 marks]
(2002 Q7)
Assume that the power rating of all globes in Q and R are identical.
How much power is dissipated by each globe in groups Q and R?
16.
[3 marks]
(2002 Q8)
One of the globes in group Q burns out.
Indicate in the box beside each group whether the globes in that group are on or off. If the
group is on, indicate whether the globe is brighter or dimmer compared to when the system is
operating correctly.
17.
[3 marks]
(2003 Q1)
The electric power for Melbourne trams is supplied at a DC voltage of 600 V. The current flows
from the overhead wire through the tram motor and returns through the metal rails. Because of
the voltage drop that occurs in the overhead wire, the wire is made up of separate 3.0-km
sections. One of these sections is shown below. A separate 600-V supply is connected to one end
only of each section.
Tram 2 is accelerating and is drawing a current of 500 A. Tram 1 is drawing a current of 200 A.
What is the current in sections P, Q and R of the wire?
18.
P
A
Q
A
R
A
[2 marks]
(2003 Q2)
The voltage at the position of tram 2 is 540 V.
How much electrical power is tram 2 using?
19.
[3 marks]
What is the resistance of 1.0 km of the overhead wire?
(2003 Q3)
20.
[3 marks]
(2003 Q4)
What is the voltage at the position of tram 1?
21.
[3 marks]
(2003 Q5)
Kim decides to design a circuit to control the light intensity of a portable lamp. The circuit
consists of a 12-V light globe rated at 18 W, a variable resistor, a 12-V battery, and a 2-amp fuse
with negligible resistance. Kim is considering two different circuits, shown as circuit A and
circuit B.
Using circuit A, what is the value of the variable resistance when the power dissipated in the
light globe is 9.0 W?
22.
[3 marks]
(2003 Q6)
When using circuit B, what is the value of the variable resistance when the fuse burns out?
23.
[3 marks]
(2003 Q7)
Which circuit, A or B, should Kim choose? Justify your answer.
24.
[2 marks]
(2004 Q1)
As a decoration for a party, Val purchased a set of 36 identical small, coloured globes connected
in three strings each with 12 globes, as shown below. The globes are designed to use the
household 240 VRMS supply.
The claim on the box said that the power used when all the globes were lit was 48 W.
What RMS current is drawn from the mains supply when all the globes are lit?
25.
[2 marks]
(2004 Q2)
What current is flowing through the globe with the circle round it, when all the globes are lit?
26.
[2 marks]
(2004 Q3)
What is the RMS voltage across each globe?
27.
[2 marks]
(2004 Q4)
What is the power rating of each globe?
28.
[2 marks]
(2004 Q5)
On the box it stated that if one globe burnt out, the rest would continue to light. To Val, as a
VCE physics student, this seemed strange. So as a test of this statement, Val removed the circled
globe.
Which of the statements below best describes the situation with the globe removed?
A. All the globes (except the one that is removed) remain lit.
B.
The middle string does not light but the other two strings light as before.
C.
The middle string does not light but the other two strings do, and are brighter than before.
D.
None of the globes is lit.
29.
[2 marks]
(2004 Q6)
Reg runs a farm in central Victoria, and has a powerful electric welder which operates from the
240 V AC household supply. When operating, the welder draws a current of 80 A. This large
current is a problem since the electricity supply comes to the workshop from the farmhouse,
which is 400 m away. The two cables that run from the farmhouse to the workshop have a total
resistance of 0.32 ohm. This means that because of the voltage drop in the wires, the voltage at
the workshop is less than 240 V, and the welder will not operate properly.
Tania, his daughter, a VCE student, knows that in electric power transmission over long
distances it is best to use high voltages.
Which two of the following statements are relevant to explaining the reason why high voltages
should be used?
A. High transmission voltages require high current.
B.
For a given power the larger the transmission voltage the smaller the current.
C.
High transmission voltage causes less radiation of electric energy.
D. To minimise power loss in the wires the current must be small.
30.
[2 marks]
(2004 Q7)
Tania realises that the problem can be solved by using transformers: one to step the voltage up
at the house, and another to step the voltage down again at the workshop. The circuit is shown
below.
In the following questions you can ignore the short connections to the transformers from the
house and workshop.
After installing the system, the voltage at the workshop was 240 V when the welder was
drawing the required 80 A. The current flowing through the wires joining T1 and T2 was 5.0 A.
The turns-ratio of transformer T2 is defined as
number of turns on secondary of transformer T2
?
number of turns on primary of transformer T2
What is the value of this ratio?
31.
[2 marks]
(2004 Q8)
What is the value of the voltage drop across the wires joining the two transformers?
32.
[2 marks]
(2004 Sample Q4)
Chee-Lin has a small portable sound system that requires 24 V AC for operation. She would like
to use the transformer below to provide this power. This transformer has two secondary
outputs, which when combined correctly provide 24 V AC. All voltages are RMS and the coils
are each wound in the same direction.
Calculate the output voltage between Q and R.
33.
[3 marks]
(2004 Sample Q5)
Complete the circuit diagram below by correctly connecting the points Q, R, S, T, U and V to
provide 24 V AC to the device.
34.
[4 marks]
(2004 Sample Q12)
Jo is a farmer, who has agreed to address the local community on the topic of power
transmission. This topic has been chosen because the community is concerned about highvoltage power lines and is considering removing all of them and replacing them with lowvoltage alternatives. Jo has sketched out a speech below aimed at convincing them that there is
a good reason for high-voltage power lines. One minor issue is that Jo needs your help to
eliminate a few incorrect words.
Below is Jo’s speech. Go through it carefully and choose the correct word to ensure that the
speech is scientifically correct.
Identify your choice by circling the correct choice.
Almost all electricity sold today is in the form of [ DC / AC ], mainly because of the
ease with which it can be [ TRANSFORMED / RECTIFIED ] from one [ CURRENT
/ VOLTAGE ] to another.
Large [ VOLTAGES / CURRENTS ] in wires produce heat and therefore energy
loss because of the resistance in the wires. To overcome this loss, power is
transmitted over large distances at [ LOW / HIGH ] voltages and correspondingly [
LOW / HIGH ] currents.
As an example, if the transmission voltage was reduced to one-tenth (1/10) of the
original voltage, and the power consumption maintained, the line losses would [
INCREASE / DECREASE ] by a factor of [ 1 / 10 / 100 / 1000 ].
35.
[2 marks]
(2004 Sample Q13)
Three groups of students are out camping. Part of their camping equipment includes a set of
12V camping lamps, each rated at 12 W. The students do not want to run the lamps off torch
batteries. Instead they intend to power the lamps from their campervan, which has two 12 V
outputs. Realising that their tents could be some distance away from the car, they have brought
three 18 m extension leads. Each lamp has a switch and is connected as shown below.
As each lamp is turned on one at a time, the students notice that the lights do not seem as bright
as when they were first tested. One of the enterprising students measures the voltage on lamp 2
and notices it is only 11 V, whereas the voltage at the campervan is 12 V. All three lights are
now turned on and left on.
Which one of the following statements (A–D) best describes the relative brightness of the three
lamps?
A. Lamp 1 is the brightest of all.
B.
Lamp 1 is the same brightness as lamp 2.
C.
Lamp 1 is brighter than lamp 3.
D.
Lamps 1, 2 and 3 are equally bright.
36.
[3 marks]
(2004 Sample Q14)
Calculate the resistance of the 18 m extension lead connecting lamp 2.
37.
[2 marks]
(2004 Sample Q15)
Calculate the voltage at lamp 3.
38.
[4 marks]
(2004 Sample Q16)
An oscilloscope is used to observe the output of an AC power adapter, which delivers 12 VRMS
when connected to a 240 VRMS, 50 Hz power source. The oscilloscope has been calibrated and
the position marked ‘O’ is at 0 V.
Calculate the voltage reading of the dashed line P.
39.
[2 marks]
(2004 Sample Q17)
What is the time difference between O and Q?
40.
[3 marks]
(2004 Pilot Q1)
Jane has been asked to give a short talk on electric power. Listed below are some key parts of
her speech. Help her prepare the speech by choosing the best alternative for the options.
Question 1
In the following indicate the answer by circling the best choice from the bolded options.
If a current-carrying wire is placed in a magnetic field, the wire experiences a force that is
maximum when the wire and magnetic field are [parallel / perpendicular] to each other.
In a similar way, when a magnet is passed repeatedly through a coil of wire, the changing
[electric / magnetic] field induces voltage across the coil. This is called electromagnetic
induction. Increasing the speed at which the magnet passes through the coil [increases / reduces
/ does not change] the amount of electromagnetic induction.
41.
[2 marks]
(2004 Pilot Q5)
A transformer as shown below is being tested. The primary coil is connected to a battery and
switch. The switch is initially open and no current is flowing in the primary coil. An ammeter is
connected to the secondary coil and initially shows no deflection. When the switch is first
closed, the ammeter needle is deflected to the right and then returns to its initial position of no
deflection.
Explain why the meter deflects when the switch is closed and then returns to the undeflected
position.
42.
[2 marks]
(2004 Pilot Q6)
The switch, which has been closed for a short time, is now returned to the open position and
remains open.
Which one of the following best describes what happens to the reading of the ammeter?
A. it deflects to the left and stays at this position
B. it deflects to the right and stays at this position
C. it deflects to the left and returns to the middle position
D. it deflects to the right and returns to the middle position
E. it does not change
43.
[2 marks]
(2005 Q9)
An electrician is planning a new power supply to a farm house. The house is 1.0 km from the
existing supply. At this supply point there is a choice of either a high voltage 11 000 VRMS AC or
a lower voltage 240 VRMS AC supply. All of the appliances in the house require 240 VRMS AC and
the expected maximum power demand (load) is 12 000 W. The owner is keen to avoid the cost
of a transformer, and so initially plans to use a 1.0 km supply line to the house from the 240
VRMS supply.
A heater in the house is rated at 1200 W. Calculate the current flowing through the heater when
it is connected to a 240 VRMS supply
44.
[2 marks]
(2005 Q10)
The electrician connects the house to the 240 VRMS supply using lines with a total resistance of
2.0 Ω. Some of the appliances in the house are turned on to test the new supply. Measurements
reveal that, under these test conditions, the current flowing is 30 A.
Calculate the power loss in the supply lines from the road to the house when the current
flowing is 30 A.
45.
[2 marks]
(2005 Q11)
What would be the voltage measured at the house when the current is 30 A?
46.
[3 marks]
(2005 Q12)
The electrician suggests that using the 11 000 VRMS supply with a step-down transformer at the
house could deliver the same amount of power to the house, with a significant reduction in the
power loss in the supply lines.
Explain why using an 11 000 VRMS rather than the 240 VRMS supply would reduce the power loss
in the lines.
47.
[2 marks]
What is VPEAK-PEAK at the 11 000 VRMS supply point?
(2005 Q13)
48.
[2 marks]
(2005 Q14)
Joan found an old transformer in her grandfather’s shed and performed some simple tests to see
if it was still working using the circuit shown below. These tests included voltage and current
measurements, and the data obtained is summarised below in the table below.
Joan’s conclusion was that the transformer still worked, but for safety reasons she chose not to
measure the current in the primary coil and assumed the voltage to be 240 VRMS.
Assuming the transformer is ideal, calculate the RMS current in the primary coil.
49.
[3 marks]
(2005 Q15)
Joan and her grandfather were discussing how a transformer works and this led to a discussion
about Faraday’s and Lenz’s laws. Joan’s grandfather stated that the two laws were essentially
the same, but Joan disagreed.
Compare and contrast Faraday’s law and Lenz’s law.
50.
[2 marks]
(2005 Q16)
As a final test of the transformer, Joan increases the load on the secondary side of the
transformer. Suddenly, it stops working. She suspects that the fuse in the primary circuit has
blown and intends to replace it.
In order to replace the fuse as safely as possible, which of the following is the best precaution
for Joan to take?
A. stand on a rubber mat
B. switch off the mains supply
C. disconnect the transformer from the mains supply
D. remove the load from the transformer
51.
[2 marks]
(2006 Q9)
A village has a maximum electrical power requirement of 100 kW. The power is supplied by an
alternator, approximately 20.0 km from the village, which generates electricity at 250 VRMS at a
frequency of 50 Hz. This is converted by a step-up transformer (T1) to 22 000 VRMS, transmitted
to the edge of the village by power lines with a total resistance of 2.0 Ω, and converted back to
250 VRMS by a step-down transformer (T2) near the village. A diagram of the system is shown
below.
What would be the current in the wires at the point marked S when 100 kW of power is being
used?
52.
[2 marks]
(2006 Q10)
Show that the current at point R is approximately 4.55 A when 100 kW of power is being used.
53.
[3 marks]
(2006 Q11)
Estimate the power loss in the high voltage transmission lines supplying transformer T2 when
100 kW of power is being used in the village. Show your working. Include the unit.
54.
[2 marks]
(2006 Q12)
Briefly explain how high-voltage transmission leads to lower power losses in the system.
55.
[2 marks]
(2006 Q13)
A number of different transformers, (A – D), are available for use as transformer T1 in the
system. Their characteristics are shown below.
Which one of the transformers, (A – D), would be suitable for use as transformer T1?
56.
[3 marks]
Explain the operation of a transformer in terms of electromagnetic induction.
(2006 Q14)
57.
[2 marks]
(2006 Q15)
The alternator fails and the village is without power. One possibility is to replace the alternator
with a DC generator but an electrician says this should not be used.
Explain why an alternator rather than a DC generator should be used in this system.
58.
[2 marks]
(2006 Q16)
Normally, the power being used in the village is 40 kW. However, as people come home, the
power use increases to 80 kW. The alternator continues to provide 250VRMS at point P.
Which one of the following (A - D) is the most likely effect on the voltage at point S?
A. The voltage would increase slightly.
B. The voltage would decrease slightly.
C. The voltage would remain the same.
D. The voltage would halve.
59.
[2 marks]
(2006 Q17)
Which one of the following graphs, (A – D), best represents the output (voltage against time) at
the alternator output terminals (P and Q).
Use the following information to answer Questions 60 - 62.
60.
[3 marks]
(2007 Q11)
A class of physics students builds a model of an electricity distribution system. The circuit
diagram of the model is shown below. Ignore the resistance of wires connecting the power
supply, transformer and globe to the transmission lines.
Assume that the transformer acts as an ideal transformer (no energy losses in transformer) of
ratio primary to secondary windings of 5:1.
The current through ammeter A1 is 0.50 A.
What would be the reading on each of the meters A2, V1 and V2?
61.
[3 marks]
What would be the power delivered at each of the points listed below?
i. At the output of the 12 VRMS power supply.
ii. At the input to the primary coil of the transformer
iii. At the globe.
(2007 Q12)
62.
[3 marks]
(2007 Q13)
The 12 VRMS AC power supply is replaced by a 12 V battery. What will be observed at the globe?
Explain this observation in terms of the operation of a transformer.
Use the following information to answer the next three questions.
Bruce’s garden has a pond with a fountain in it. Bruce buys a floodlight to illuminate the
fountain. The resistance of the floodlight filament is 3.0 Ω when operating.
63.
[3 marks]
(VCE 2008 Q11)
First Bruce tests the floodlight before he installs it. He tests it by applying 12 VRMS across the
floodlight. What is the power used in the floodlight when supplied with a voltage of 12 VRMS?
Show working.
64.
[3 marks]
(VCE 2008 Q12)
Bruce now installs the floodlight.
The electricity supply for the floodlight is supplied from the house using two wires (as shown
below). Each of the two wires that connect the supply has a resistance of 0.50 Ω.
When operating, what is the voltage across the floodlight?
Show working.
65.
[3 marks]
(VCE 2008 Q13)
Bruce decides that the light is not bright enough and installs a second identical floodlight (as
shown in the circuit below)
What is the current now fl owing through the wire at point A?
Show working.
Use the following information to answer the next two questions.
Jamie has a study lamp (shown below) that uses a 40 W globe that operates at 18 VRMS. The
lamp plugs into the 240 VRMS supply, and a transformer (assumed to be ideal) in the base of the
lamp provides the 18 VRMS for the globe.
The secondary coil of this small transformer has 30 turns.
66.
[2 marks]
How many turns are on the primary coil?
Show working.
(VCE 2008 Q14)
67.
[3 marks]
When operating, what is the current flowing in the primary coil?
Show working.
(VCE 2008 Q15)