304
Electrical and Electronic Measurements and Instrumentation
33. Explain the circuit of a multimeter for measure­
ment of a.c. voltages. Why are multimeters provided
with a separate scale for low voltage a.c. range ?
Explain why a rectifier type of voltmeter may have
a uniform (or linear) a scale on the high voltage
ranges, but generally has a non-linear scale for low
voltage ranges.
34. Compare the effects of circuit loading when using
an a.c. voltmeter with half wave rectification
against those when using an a.c. voltmeter with
full wave rectification.
35.
Draw up a table to list the suitability for use on d.c.
and a.c. and major uses of the following types of
instruments :
(i)
(ii)
(ill)
PMMC type
Moving iron type
Electrodynamometer type
(ib) Thermocouple type
(ib) Electrostatic type
(v) Rectifier type.
Unsolved Problems
1. A moving coil instrument has the following data :
number of turns = 100, width of coil =20 mm, depth
of coil = 30 mm, flux density in the gap = 0.1
Wb/m . Calculate the deflecting torque when
carrying a current of 10 mA. Also calculate the
deflection if the control spring constant is 2 x IO-6
Nm/degree.
[Ans. 60 x 10-6 Nm, 30°]
2. The following data refers to a moving coil
voltmeter :
(b) The value of the shunt resistance for the instru­
ment to give a full-scale deflection of 50 A.
[Ans. 25 A ; 0.001001 Q]
5. A moving-coil instrument has at normal tempe­
rature a resistance of 10
and a current of
45 milliampere gives full scale deflection. If its
resistance rises to 10.2 Q due to temperature
change, calculate the reading when a current of
2000 A is measured by means of a 0.225 x IO-3 A
shunt of constant
percentage error ?
resistance. What is the
[Ans. 44.1 mA, - 1.96%]
Resistance, 10,000 ohm ; dimensions of coil 30 mm
x30 mm; number of turns on coil, 100; flux density
in gap, 0.08 Wb/m ; spring constant, 3 x 10-6 Nm
6. The coil of a moving-coil voltmeter is 40 mm x 30 mm
per degree. Find the deflection produced by a
voltage of 200 V.
[Ans. 48°]
wide and has 100 turns wound on it. The control
spring exerts a torque of 0.25 x 10~3 Nm when the
3. A moving coil milli-voltmeter has a resistance of
200 Q and the full scale deflection is reached when
a potential difference of 100 mV is applied across
the terminals. The moving coil has effective
dimensions of 30 mm x 25 mm and is wound with
2
100 turns. The flux density in the gap is 0.2 Wb/m .
Determine the control constant of the spring if the
final deflection is 100° and a suitable diameter of
copper wire for the coil winding if 20 percent of the
total instrument resistance is due to the coil
_Q
winding. Resistivity of copper is 1.7 x 10 Qm.
[Ans. 0.075 x 10 6 Nm/degree ; 0.077 mm]
4. The coil of a measuring instrument has a resistance
of 1 Q, and the instrument has a full scale deflection
of 250 V when a resistance of 4999 Q is connected in
series with it. Find
(fl) The current range of the instrument when used
as an ammeter with the coil connected across a
shunt of 1/499 Q, and
deflection is 50 divisions on the scale. If the flux
density ^of the magnetic field in the air-gap is
1 Wb/m estimate the resistance that must be put in
series with the coil to give 1 volt per division.
Resistance of voltmeter is 10,000 Q.
[Ans. 14,000 Q]
7. A direct voltage of 240 V is applied to a uniform
200 Q resistor abc. A 40 Q resistor is tapped across
ab. Find the resistance of ab in order that 1 A flows
in the 40 Q resistor.
[Ans. 71.65 Q]
8. A moving-coil instrument has a resistance of 5 Q
between terminals and full scale deflection is
obtained with a current of 15 mA. This instrument
is to be used with a manganin shunt to measure
100 A at full scale. Calculate the error caused by a
10°C rise in temperature :
(fl) When the internal resistance of 5 Q is due to
copper only.
(b) When a 40 manganin swamping resistance is
used in series with a copper coil of 1Q resistance.
Analog Ammeters, Voltmeters and Ohmmeters
305
The resistance temperature co-efficients of copper
and manganin are 0.4%/°C and 0.015%/°C rise
respectively.
[Ans. 3.7% low : 0.8% low]
9.
10.
Design a multi-range ammeter with ranges of 1 A,
5 A, 25 A and 125 A employing individual shunts
in each case. A d'Arsonval movement with an
internal resistance of 730 Q and a full scale current
of 5 mA is available.
[Ans. 3.67 Q, 0.73 Q, 0.146 Q, 0.0292 Q]
inductance of a moving iron ammeter is given
by : L = (0.01+ CO)2 mH, where 0 is the deflection
15. The
from zero position in degree. The angular
deflections of the instrument corresponding to 1.5
and 2 A are respectively 90° and 120°. Find the
value of C.
[Ans. -0.0474 x 10-3]
16. The relationship between inductance of a moving
iron ammeter, the current and the position of the
pointer is as follows :
A basic d'Arsonval movement with a full scale
reading of 50 pA and an internal resistance of
1800D is available. It is to be converted into a
0 - 1 V, 0 - 5 V, 0 - 25 V and 0 - 125 V multi-range
voltmeter using individual multipliers for each range.
Calculate the value of the individual multipliers.
[Ans. 18.2 kQ, 98.2 kQ, 498.2 kQ, 2498.2 kQ]
a basic
d'Arsonval movement of 50 p A with an internal
resistance of 2000 Q. The multi-voltmeter ranges of
this instrument are 0 - 2.5 V, 0 - 10 V, 0 - 50 V,
0 - 250 V, 0 -1000 V and 0 - 5000 V. The instrument
utilizes the potential divider arrangement shown
in Fig. 9.11. Calculate the resistances values of Rv
R2, Ry R4, R5 and R6.
[Ans. 48 kQ, 150 kQ, 800 kQ, 4 kQ, 15 kQ, 80 kQ]
Reading
(A)
11. The Simpson multimeter model 260 uses
12. Design a series type ohmmeter (as shown in
Fig. 9.13). The basic movement requires a current
of 1.0 mA for full scale deflection and has an
internal resistance of 50 Q. The internal battery has
a voltage of 3.0 V. The desired value of half scale
resistance is 2000 Q. Calculate
(a) The values resistances R} and R9.
j
Deflection
(degree)
Inductance
(VB)
0.8
16.5
527.8
1.0
26
573.9
1.2
36
575
1.4
46.5
576.2
1.6
57
577.3
1.8
70
578.35
579.45
2.0
2.0
|j
Calculate the deflecting torque when the current is
1.5 A and 2.1 A.
[Ans. 6.45 x 10-6 Nm, 5.73 x 106 Nm]
17. The control spring of moving iron ammeter exerts
a torque of 0.5xlO-6 N-m/degree when the
deflection is 52°. The inductance of the coil varies
with pointer deflection according to :
Deflection (degree)
20
40
60
Inductance (p.H)
659
702
752
80
|
(b) The range of values of R2, if the battery voltage
may vary from 2.7 V to 3.1 V. Use value of R1 as
calculated in (fl).
[Ans. (fl) R, = 1966.7 Q, 100 Q (b) 142.8 - 90.9 Q]
13.
A shunt type ohmmeter, with circuit as shown in
Fig. 9.14 uses a basic meter with a full scale current
of 2 mA and an internal resistance of 25 Q. The
battery has an emf of 1.5 V. Find
(a) The value of resistance R}
(b) At what point (in percentage of full scale) will
100 Q be marked on the scale ?
[Ans. (fl) 725 Q. (b) 80.5% A]
14.
The inductance of a certain moving iron ammeter
/1
is 8 + 40 — 0 pH where 0 is the deflection in
k
2 7
radian from the zero position. The control spring
torque is 12X10-6 N-m/rad. Calculate the scale
positions in radian for currents 1, 2, 3, 4 and 5 A
and discuss the scale shape obtained.
[Ans. 0.16, 0.571, 1.09, 1.6, 2.04 rad]
Determine the current passing through the meter.
[Ans. 0.63 A]
coil of a 150 V moving iron voltmeter
has a resistance of 400 ohm at 15°C and an
inductance of 0.75 H. The current for full scale
deflection is 0.05 A.
18. The copper
The temperature coefficients of resistance for
copper and eureka at 15°C are 0.004/°C and
0.00001/C0 respectively.
Calculate :
(a) The percentage increase of resistance of this
instrument per degree rise in temperature
(b) The indication when 150 V at 100 Hz is applied,
the instrument having been previously cali­
brated on direct current.
[Ans. 0.0542%, 148.17 V]
for a maximum reading of
120 V has an inductance of 0.6 H and a total
19. A soft-iron voltmeter