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AL-LQ-Circuits / p.1
1.
(95-I-8)
(a)
A student uses the circuit shown below to measure the resistance of a resistor, R, with an
unknown order of magnitude. The voltmeter and the ammeter are ordinary moving-coil meters
used in school laboratories. He first connects K to X with a flying lead and then to Y.
(i)
Describe the change in the readings of the voltmeter and the ammeter, if any, when the
flying lead from K is moved from X to Y for
(ii)
(I)
R of a few ohms,
(1 mark)
(II)
R of a few kilo-ohms.
(1 mark)
The student decides to connect K to Y. The voltmeter and the ammeter read 6 V and 0.8 mA
respectively.
(b)
(I)
Comment, with reasons, on his choice of connecting K to Y.
(II)
Find the true value of R if the resistance of the ammeter is
(2 marks)
20 .
(1 mark)
The circuit below is employed to measure the e.m.f., E, and the internal resistance, r (a few ohms),
of a dry cell. (Assume the voltmeter and the ammeter used are ideal.)
(i)
If the full-scale deflection of the ammeter is 500 mA, suggest which ranges of the voltmeter
and the rheostat it would be suitable to use.
(ii)
(1 mark)
The voltmeter readings, V, and the ammeter readings, I, obtained for different rheostat
settings are used to plot the graph below.
Express V in terms of E, I and r. Hence deduce from the graph the e.m.f. and the internal
resistance of the cell.
(3 marks)
(iii) It can be proved that when the resistance of the rheostat equals the internal resistance of the
cell, maximum power output from the cell would be obtained. Find an expression of this
maximum power output in terms of E and r, and calculate the corresponding output
efficiency of the cell.
(3 marks)
AL-LQ-Circuits / p.2
2.
(97-I-4)
(a)
The figure shows three identical cells connected with a 10 k resistor. A student uses a CRO
and a moving-coil voltmeter in turn to measure the potential difference across PQ, the readings
being 4.5 V and 4.1 V respectively.
(i)
Account for the difference in the readings.
(ii)
Estimate the resistance of the voltmeter. What would the reading be if the voltmeter is
connected across XQ?
(3 marks)
(3 marks)
(b) he figure shows part of the internal structure of a typical multimeter. It has a coil connected to a
shunt built from resistors
resistances of
R1 and R2 , and a series of voltage multipliers R3 and R4 . The
R1 , R2 and R3 are 9.8 k , 200  and 48k respectively. A rotary switch S
enables the various full-scale values of current or voltage to be chosen.
(i)
Calculate the resistance of the coil and the current flowing through it for full-scale deflection.
Show your working.
(ii)
Calculate the resistance of
(4 marks)
R4 .
(2 marks)
(iii) In the spaces provided in the above figure, add two components to the circuit so that the
multimeter can be used to measure resistance between its input terminals when switch S is
set at X. Describe briefly how to adjust for zero ohm position.
(3 marks)
AL-LQ-Circuits / p.3
3.
(01-IB-8)
Figure 8.1 shows a circuit for investigating the current delivered by a battery and its terminal voltage. A battery of
e.m.fε and internal resistance r is connected through an ammeter to a variable resistor R. The terminal voltage is
measured by a high-resistance voltmeter. The resistance of the ammeter is negligible compared to that of R.
Figure 8.1
The ammeter reading I and voltmeter reading V for different values of R are tabulated as follows:
I (A)
V (V)
V/I()
-1
1/I(A )
0.80
3.52
0.50
4.46
0.40
4.76
0.32
5.02
0.25
5.23
(a)
Express V in terms of ε, I, r. Explain why V increases as I decrease.
(b)
Complete the above table and plot a graph of V/I against 1/I in order to determine the e.m.f. and the
internal resistance of the battery.
(c)
Suggest a graphical method to determine the resistance value of R necessary for the battery to deliver
maximum output power.
Both the ammeter and voltmeter used are converted from the same kind of basic meter, which has a scale with
100 divisions; its current sensitivity is 0.01mA per division and the voltage sensitivity is 1.0mV per division.
(d)
Find the resistance of the basic meter and describe how a convert such a meter into
(i)
an ammeter of full-scale deflection 1A; and
(ii)
a voltmeter of full-scale deflection 6V
Give the value(s) of the component(s) you would use.
(e) Figure 8.2 shows a circuit in which the converted meters in (d) are used for measuring a resistance R1 of
1kΩ. Would the measured value of R1 obtained from the meter readings be smaller than, close to or
greater than the actual value? Find the percentage error in the measured value
.