As h 13c Alternatingcurrents

8/12/2019 As h 13c Alternatingcurrents

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Direct and alternating current

Direct current (d.c.)This is electric current that does not changedirection in a circuit.

Note: Direct current may change in size.Alternating current (a.c.)This is electric current that repeatedlyreverses its direction.


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The peak-to-peak value (2 V 0 or 2 I 0 ) is equal to the maximumvariation in current or pd.With a pure a.c. this is equal totwice the peak value. The UKs a.c. supply has a peak -to-peak voltage of 650V (2 x325V)

The period of the a.c. is the timetaken to complete one cycle ofvariation.The UKs a.c. supply has a periodof 0.02s or 20ms. The sinusoidal variation of the voltage

of the UKs domestic mains supply.


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The heating effect of a.c.

The heating effect of current isindependent of the direction ofcurrent flow.

Power is the rate of heattransfer.With a resistor, R :P = I 2 R

With a varying current:P = < I 2 > R


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With sinusoidal variation: < I 2 > = I 0 2

And so: P = I 0

2 R

current

power meanpower


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Root mean square valuesThe root mean square(rms) value of analternating current is equalto the value of directcurrent that would give thesame heating effect as thealternating current in thesame resistor.

if:I

rm s 2

R = I

0 2

Rthen: I rm s 2 = I 0 2

and so:I

rm s = I 0 / 2

also with pds:V rm s

= V 0 / 2

and: P = I rm s V rm s


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QuestionCalculate the rms values of the UK and USA mainsvoltage supplies if the peak values, V 0 are 325V and155V respectively.


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Answers:

V 0

/ V I 0 / A R / V

rm s

/ V I rm s

/ A P / W

12 4

50 230 4.6

155 5.5

1.41 0.50

0.30 20

Complete:


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The Oscilloscope


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An oscilloscope (of traditional design) consists of aspecially made electron tube and associated controlcircuits.

An electron gun at one end of the glass tube emitselectrons in a beam towards a fluorescent screen at theother end of the tube. Light is emitted from the spot on thescreen where the beam hits the screen.

The position of the spot on the screen is affected by the pdacross either pair of deflecting plates (Y 1Y2) and (X 1X2).

The X-plates deflect the beam horizontally, the Y-platesvertically. In both cases the deflection of the beam isproportional to the applied pd.


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The oscilloscope graph scales Y-AXIS

Potentialdifference

Scale determinedby the Y -GAIN

control

Typical setting:1V / cm

X-AXIS

Time

Scale determined by the X -GAIN or TIME -BASE control

Typical setting: 0.1s / cm

cm squares+ V

0V

- V


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Displaying a waveform1. The time base

The X-plates are connected to theoscilloscopes time base circuit.

This makes the spot move acrossthe screen, from left to right, at aconstant speed.

Once the spot reaches the righthand side of the screen it isreturned to the left hand sidealmost instantaneously.

The X-scale opposite is set so that

the spot takes two milliseconds tomove one centimetre to the right.(2 ms cm -1).


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Displaying a waveform2. Y-sensitivity or Y-gain

The Y-plates are connected tothe oscilloscopes Y -input.

This input is usually amplifiedand when connected to the Y-plates it makes the spot movevertically up and down thescreen.

The Y-sensitivity opposite is setso that the spot movesvertically by one centimetre fora pd of five volts (5 V cm -1).

The trace shown appears whenan alternating pd of 16V peak-to-peak and period 7.2 ms isconnected to the Y-input withthe settings as shown.


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Measuring d.c. potential difference

Diagram a shows the trace for pd = 0V.

Diagram b shows the trace for pd = +4VDiagram c shows the trace for pd = -3V.

All three diagrams below show the trace with the time baseon and the Y-gain set at 2V cm -1 .


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Measuring a.c. potential differenceLet the time base setting be 10ms cm -1 and the

Y-gain setting 2V cm-1

.In this case the waveform performs onecomplete oscillation over a horizontal distanceof 2 cm.Therefore the period of the waveformis 2 x 10ms

period = 20 msas f requency = 1 / per iodfrequency = 1 / 0.020s= 50 Hz.

The peak-to-peak displacement of the waveformis about 5cm.Therefore the peak-to-peak pd is 5 x 2VPeak-to-peak pd = 10V


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Measuring a time intervalThe diagram opposite shows how anoscilloscope could be used to measure thespeed of a pulse of ultrasound.

A trigger pulse is sent from the oscilloscope tothe transmitter. At the same time the spot ismoved across the screen by the time base.

When the receiver, which is connected to theY-input, detects the pulse a deflection appearson the screen.

If the time base had been set to 2 ms cm -1 thenthis pulse is shown to have taken about 7 ms totraverse the gap between the transmitter andreceiver.

Note: The time taken for the pulse to travel asan electric current in the wires is usually sosmall (< 1 microsecond) that it can be ignored.


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Question 1

Measure the approximate period, frequency and peak-to-peak pd of the traceopposite if:Time base = 5ms cm -1

Y-gain = 5V cm -1

period = 50ms / 6 8.7ms

frequency 115 Hzpeak-to-peak pd 20V


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Question 2Measure the approximate

period, frequency and peak pd of the trace opposite if:Time base = 2ms cm -1

Y-gain = 0.5V cm -1

period = 20ms / 12 1.7msfrequency 600 Hz

peak pd 1.3V


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Question 3

The trace shows how awaveform of frequency286 Hz and peak-to-

peak pd 6.4V is

displayed.Suggest the settings ofthe time base and Y-gain amplifier.

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As h 13c Alternatingcurrents