Download Exercise 9 Revision on A.C(III)

C.K.Cheung
Exercise9 ( A.C. (III))
5.
X
search coil
R
to CRO
a.c.
source
r
A
Y
Figure 5
A student fixes a straight wire XY, about 1 m along, on a table and connects it in series
with an a.c. power supply, a rheostat and an ammeter, as shown in Figure 5. He also
connects a search coil to a CRO. Starting at a position near the middle of the straight
wire, he places the search coil flat on the table at various distances r form the wire and
measures the corresponding peak-to-peak voltages V on the CRO.
__
1 /V -1
V
1 000
900
800
700
600
500
400
300
200
100
0
0.1
0.2
0.3
0.4
0.5
r /m
Figure 6
(a) The student plots 1/V against r, as shown in Figure 6.
(i) It is found that the first six data points lie on a straight line. What
experimental conclusion can you draw about the variation of the magnetic
flux density due to the alternating current at various distances from the wire?
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C.K.Cheung
(ii)
(b) (i)
Explain why the data points for r > 0.3 m depart from the fitted straight line.
In this experiment, the variation of current with time t in the long straight wire
is I0 sin (2ft), where I0 is the peak current and f the a.c. frequency. If the
search coil is of area A and consists of N turns, find an expression for the
peak-to-peak voltage V induced in the search coil when r  0.3 m.
(ii) If I0 = 14.1 A, f = 50 Hz, A = 3.14  10-4 m2 and 0 = 1.26  10-6 H/m,
estimate the number of turns in the search coil.
(c) Another student argues that the results obtained in this experiment are not accurate
because the influence of the earth magnetic field has not been considered. In this
argument correct?
Give a brief explanation.
(12 marks)
85' IIB
(6). The input terminals of a C.R.O., on both the d.c. and a.c. settings, are thought to have
(1) a resistor R of resistance 1 - 10 M, and
(2) a capacitor C of capacitance 10 - 100 pF
connected internally in parallel. From the following experiments it is intended to
confirm the presence of these components and derive their values as accurately as
possible.
Note :
R1
R 1 and R 2 both
have a resistance of
1.00 M  .
R2
K
9.00 V battery
Figure 4
(a) The circuit used is shown in Figure 4. Using the d.c. setting of the C.R.O., the
horizontal trace on the screen is observed to move to a level corresponding to 3.00
V when key K is closed. Determine the value of one of the components [either (1)
or (2)], briefly explaining your reasoning.
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C.K.Cheung
(b) The 9.00 V d.c. supply is now replaced by an a.c. signal generator and the
frequency and output adjusted to give a suitable waveform on the C.R.O. (using a.c.
setting) so that the peak-to-peak voltage can be measured accurately. The signal
generator is found to have an output of 7.07 V r.m.s. and a frequency of 3.20 MHz.
(i)
Considering only the circuit consisting of the signal generator and the resistors
R1 and R2 (i.e. ignoring any loading effect of the C.R.O.), write down the
peak-to-peak voltage value of the waveform you might expect.
(ii)
Now using the value you found in (a), give a more accurate estimate of the
peak-to-peak voltage observed on the C.R.O.
(iii) However, the actual measured peak-to-peak voltage observed on the C.R.O.
screen was only 20 mV. Hence, estimate the value of the other C.R.O. input
component [(1) or (2)], briefly explaining your reasoning.
(9 marks)
83 IIB
5.
S
R
lamp A
To Y1 trace
50 Hz
a.c.
supply
L
L
To Y2 trace
500 
lamp B
To oscilloscope
earth
Figure 4
Figure 5
(a) In the circuit in Figure 4, L is a very large inductance. With switch S closed,
resistor R is adjusted until the two lamps glow with equal brightness. Assume that
this adjustment has been made and that switch S has been opened, and left open for
some considerable time. If the switch is now closed, what will be observed?
Explain.
(b) The large inductance is now connected in series with a 500  resistor and a 50 Hz
a.c. supply as shown in Figure 5. The Y1 and Y2 inputs of a double trace
oscilloscope are connected as shown. (Note that the earth connection is common
to both inputs.) With the time base set to 2 ms/cm the stationary pattern shown in
Figure 6 is obtained.
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C.K.Cheung
Y2 trace
Y1 trace
1 cm
Figure 6
Calculate a value for L, giving a vector (phasor) diagram of the p.d. across the
inductance and the resistor.
(Assume that the inductance has negligible
resistance.)
(c) Sketch the pattern you would expect to observe if the connections to the
oscilloscope earth and the Y2 input were interchanged.
(10 marks)
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