WheatstonE Bridge & Ohm’s Law
Experiment-438
S
COMPARISION OF RESISTIVITY
MEASURED USING CAREY-FOSTER
BRIDGE (WHEASTONE’S LAW)
AND THE DIRECT METHOD
(OHM’S LAW)
Jeethendra Kumar P K and Sowmya*
KamalJeeth Instrumentation & Service Unit, JRD Tata Nagar, Bengaluru-560092, INDIA
*Dept of Electronics, Mangalore University, Mangalagangothri-574199, Mangalore, INDIA
Email: labexperiments@rediffmail.com
Abstract
The resistivity of nichrome and mangnin wires, are determined using two
fundamental laws of electricity in two different instruments. The resistivity
determination using Ohm’s law appears to be faster and easier. The resistivity
values obtained are in very good agreement with the known standard values.
Introduction
Electrical conductivity is a fundamental property of metals. A metal in the form of wire
as well as bulk material exhibits this property. Lower the value of resistivity, higher is
the conductivity which means that the material conducts more electricity, and vice
versa. This property of metals assumed importance when semiconductor was invented
in 1827 by Georg Simon Ohm. Hence search for a method for determining resistivity
became very important. There are several experiments for measurement of resistivity.
Among these Carey-Foster Bridge or Meter Bridge method is quite common which
makes use of Wheatstone’s bridge principle. This is purely an analog method which has
been followed historically [1].
Digital technology offers numerous varieties of digital meters that can also be used to
determine resistivity. Use of such meters makes the measurement of resistivity simple
and fast as there are no inter- connections between various parts of the apparatus. In
this method instead of Wheatstone’s law Ohm’s law is made use of.
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KAMALJEETH INSTRUMENTS
WheatstonE Bridge & Ohm’s Law
Theory
Resistance of a wire is given by the equation
୐
R = sୟ
…1
where
‘L’ is the length of the wire
‘s’ is the specific resistance, or resistivity, of the wire, and
‘a’ is the cross sectional area of the wire.
Hence resistivity, s, is given by
s=
ୖୟ
୐
…2
Since R is measured in Ohms, L is measured in meter and cross sectional area is
measured in m2; resistivity has the dimension Ω.m. Digital Ohm- meters that can
measure low resistance < 10Ω can be used to measure resistance R and for a given
length of wire and knowing its radius , resistivity can be measured easily. In the new
direct method we measure the resistance R of the wire by passing a known current
through it and measuring the potential across it. The ratio V/I provide value of
resistance. One should pass a small current so that there is no heating effect on the
wire.
Hence we need the dimensional parameters (a, L) of the wire to determine the
resistivity of the wire. Wire has low value of resistivity hence any meter or method that
can measure small values of resistance (<10Ω) can be used to determine the resistance of
the given wire.
In the second method using Wheatstone’s law, a Carey-foster bridge is used to
determine the resistance of the wire sample. By the method of bridge balance, the
unknown resistance of the wire is determined. A Wheatstone’s bridge has four arms
with four resistances as shown in Figure-1
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KAMALJEETH INSTRUMENTS
WheatstonE Bridge & Ohm’s Law
Figure-1: Wheatstone’s bridge
A meter bridge or Carey-Foster bridge has two gaps in which one can insert a known
resistance R and unknown resistance P. The central wire of the bridge forms the
resistance, hence the total length (=Q+S) of the central wire is given by
Q+S = length of central wire =1m
…3
The power supply (Electronic Laclanche cell, 1.46V) is connected across the central wire
at A&B, the other two nodes (CD) of the Wheatstone’s bridge are connected to
galvanometer and pencil jockey in series. By touching the central wire with pencil
jockey completes the Wheatstone’s bridge. Hence the galvanometer will show
deflection when the central wire makes contact with the jockey. IF ‘x’ is balancing
length where deflection in galvanometer is zero, then
Q = x and
S = 1-x
Substituting these values in the Bridge equation
୔
୕
ୖ
=
…4
ୗ
௉ೠ೙ೖ೙೚ೢ೙
௫
=
ோೖ೙೚ೢ೙
ଵି௫
…5
The unknown resistance P can be determined as
ୖ௫
P = ଵି௫
…6
Where ‘x’ is balancing length from node A and R is the known resistance (a 0.1-10 Ohm
two dial MFR resistance box is used). Hence the resistance of the wire can be
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KAMALJEETH INSTRUMENTS
WheatstonE Bridge & Ohm’s Law
determined and knowing the dimensional parameters of the wire, its resistivity can be
determined.
In the direct method a constant current I, is passed through the sample wire and the
voltage V, developed across it is measured, the ratio of V/I gives the value of resistance
R, and resistivity of nichrome and mangnin wires obtained are compared.
Apparatus used
To determine resistivity using Carey-Foster Bridge we have used Carey-Foster Bridge,
electronic standard cell or a Laclanche cell, mangnin coil, nichrome coil, and
galvanometer. Figure-2 shows the experimental set-up used.
Figure-2: Experimental set-up using Carey Foster Bridge
To determine resistivity using direct method we have used: The experimental set-up
consists of digital milli-voltmeter 0-200mV, digital milli-ammeter 0-200mA, constant
current source, mangnin coil, and nichrome coil. Figure-3 shows the coil used mangnin
and nichrome coils used in the experiment.
Experimental procedure
The experiment consists of two parts, namely
Part-A: Determination of resistivity of nichrome and mangnin wires using CareyFoster bridge (based on Wheatstone’s law)
Part-B: Determination of resistivity of nichrome and mangnin wires using direct
method (using Ohm’s law)
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KAMALJEETH INSTRUMENTS
WheatstonE Bridge & Ohm’s Law
Figure-3: Mangnin and nichrome coils used in the experiment
Figure-4: Experimental set-up using Ohm’s law
Experimental procedure
The experiment consists of two parts, namely
Part-A: Determination of resistivity of nichrome and mangnin wires using CareyFoster bridge (based on Wheatstone’s law)
Part-B: Determination of resistivity of nichrome and mangnin wires using direct
method (using Ohm’s law)
Part-A: Determination of resistivity of nichrome and mangnin wires
using Carey-Foster bridge (based on Wheatstone’s law)
1. The diameter and length of the two wires selected for the experiment is noted
and their cross sectional areas are calculated and presented in Table-1.
2. The nichrome coil whose resistance has to be determined is connected across the
gap P and a resistance box 0.1-10 Ω is connected across the gap R. Remaining
circuit connections are made as shown in Figure-1.
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KAMALJEETH INSTRUMENTS
WheatstonE Bridge & Ohm’s Law
3. R =3Ω is set in the resistance box and the pencil jockey is made to establish
contact with both ends of the central wire to show galvanometer deflection in the
opposite side. This indicates that the circuit connection is made properly.
4. The pencil jockey is moved over the central experimental wire to get zero
deflection in the galvanometer.
Table-1: Wires and their dimensional parameters
Parameter
Nichrome
Mangnin
Length ‘L’ (m)
1
1
Radius ‘r’ (mm)
0.273
0.271
2
-7
Area (m )
2.34x10
2.30x10 -7
5. The balancing length ‘x’ is obtained as
x = 62.8, hence Q= 0.628m
S = 1-Q = 1-0.628 = 0.372m
Hence unknown resistance P may be calculated using Equation-4 as
ୖ୶
P = ଵି୶
=
ଷ௫଴.଺ଶ଼
଴.ଷ଻ଶ
= 5.06Ω
6. The experiment is repeated by increasing the value of the known resistance R in
steps by 1 Ω up to the maximum value of 10Ω and in each case the balancing
length for obtaining zero-deflection is noted and recorded in Table-2 and the
value of unknown resistance ‘P’ is calculated using Equation-4. The readings
obtained are tabulated in Table-2.
Table-2: Balancing length for Nichrome wire
ࡾ࢞
Known
Balancing length (1-x) m
(Ω)
P=
૚ି࢞
resistance R (Ω)
x (m)
3
0.628
0.372
5.06
4
0.559
0.441
5.07
5
0.503
0.497
5.06
6
0.459
0.541
5.09
7
0.420
0.580
5.06
8
0.391
0.609
5.10
9
0.360
0.640
5.06
10
0.338
0.662
5.10
Average value of P
5.075Ω
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KAMALJEETH INSTRUMENTS
WheatstonE Bridge & Ohm’s Law
7. The resistivity of Nichrome wire is calculated using Eqution-4 as
ρ=
୔ୟ
୐
=
ହ.଴଻ହ௫ଶ.ଷସ௫ଵ଴ షళ
ଵ
= 1.18‫ݔ‬10ି଺ = 1.18µΩm
8. The Nichrome wire is now replaced with the Mangnin wire whose dimensions
are given in Table-1 and the experiment is repeated by varying R in the range 310Ω. The balancing lengths obtained are tabulated in Table-3.
Table-3: Balancing lengths for the mangnin wire
ࡾ࢞
Known
Balancing length (1-x) m
P = ૚ି࢞ (Ω)
resistance R (Ω)
x(m)
3
0.368
0.632
1.74
4
0.304
0.696
1.74
5
0.260
0.740
1.75
6
0.226
0.774
1.75
7
0.201
0.799
1.76
8
0.179
0.821
1.74
9
0.165
0.835
1.77
10
0.150
0.850
1.76
Average value of P
1.751Ω
9. The resistivity of Mangnin wire is calculated using Eqution-4 as
ρ=
୔ୟ
୐
=
ଵ.଻ହଵ௫ଶ.ଷ௫ଵ଴షళ
ଵ
= 1.18‫ݔ‬10ି଺ = 0.402µΩm
Part-B: Determination of resistivity of nichrome and mangnin wires
using the direct method (based on Ohm’s law)
10. The experimental set-up shown in Figure-4 is switched on and the Nichrome
wire coil whose resistance is to be determined in connected across the terminal
provided.
11. The current through the coil is set to 2mA and voltage developed across the wire
is noted and tabulated in Table-4.
I= 2mA, V= 10.9
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KAMALJEETH INSTRUMENTS
WheatstonE Bridge & Ohm’s Law
12. The experiment is repeated by varying the current in suitable steps up to the
maximum value 30mA and the corresponding voltage developed is noted and
recorded in Table-4.
13. A graph is drawn, with current, I, along the X-axis and voltage, V, along the Yaxis, as shown in Figure-5 and the slope of the straight line thus obtained gives
the value of the resistance of the Nichrome wire as slope = Value of the
unknown resistance,
P = 5.295Ω
14. Resistivity of Nichrome wire is calculated using Equation-4
ρ=
୔ୟ
୐
=
ହ.ଶଽହ௫ଶ.ଷ௫ଵ଴షళ
ଵ
= 1.217‫ݔ‬10ି଺ = 1.21µΩm
Table-4: Current and voltage values for the Nichrome wire
Current I(mA)
Voltage (mV)
0
0
2
10.9
4
21.4
6
31.9
8
42.8
10
53.3
12
63.8
14
74.3
16
85.1
18
95.2
20
106.1
24
127.7
26
138.0
30
158.8
Slope V/I= 5.295Ω
18. The experiment is repeated with mangnin coil and the calculated values of
current and resistance are recorded in Table-5 and plotted in Figure-6 which
shows the V-I curve for the Mangnin wire.
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KAMALJEETH INSTRUMENTS
WheatstonE Bridge & Ohm’s Law
Voltage (mV)
200
150
100
50
0
0
10
20
30
40
Current (mA)
Figure-5: V-I curve for Mangnin wire
19. Experiment is repeated with mangnin coil and voltage current and resistance
calculated are shown in Table-4 and Figure-5 shows the V-I curve for Mangnin
wire
Resistivity of the Mangnin wire is calculated using Equation-4 as
ρ=
୔ୟ
୐
=
ଵ.଻ଷଷ௫ଶ.ଷ௫ଵ଴షళ
ଵ
= 0.398µΩm
20. Experiment is repeated with the nichrome wire and the resistance of wire and
resistivity are calculated. Table-6 shows the V-I relation and it is plotted in
Figure-6. The slopes of the straight line give resistance of wire used.
Table-5: Current and voltage values for Nichrome wire
Current I(mA)
Voltage (mV)
0
0
2
3.5
4
7.0
6
10.4
8
13.9
10
17.3
12
20.8
14
24.3
16.1
27.9
18
31.1
20
34.6
24
41.5
28
48.6
30
52.1
Slope =1.733Ω
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KAMALJEETH INSTRUMENTS
Voltage (mV)
WheatstonE Bridge & Ohm’s Law
60
50
40
30
20
10
0
0
10
20
30
40
Current (mA)
Figure-6: V-I curve for the Nichrome wire
Result
The resistivity of Nichrome and Mangnin wires calculated using two different methods
are tabulated in Table-6
Table-6: Experimental results
Nichrome
Mangnin
Parameters
Wheatstone’s Ohm’s
Std
Wheatstone’s Ohm’s
Std
Resistivity
s
or
1.180
1.217
1.10
0.40
0.398
0.482
ρ(µΩm)
Resistance per meter
5.075
5.295
5.47
1.751
1.733
1.73
(Ω)
Discussion
The values of resistivity obtained by the two methods indicate that both the methods
are suitable for determination of resistivity. The direct method is much simpler and
faster. The Wheatstone’s bridge method requires many interconnections and so it may
be difficult to perform by students. Hence one may chose the second method for
determination of resistivity which can be interfaced with a computer so that it can
directly give the value of resistivity.
The maximum value of current passing through the wire is limited to 30 mA in the
direct method because excessive current may heat the wire and its resistance may
change due change in the temperature. In the case of Wheatstone’s bridge the current is
decided by the central wire and generally it gets heated up when performing
experiment. One can feel this touching the central wire.
The standard value coated in Table-6 is without knowing the exact composition of the
material of the wire. The resistivity changes with the composition of the material, even
for 1% changes in composition of a material its resistivity will be significantly different.
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KAMALJEETH INSTRUMENTS
WheatstonE Bridge & Ohm’s Law
Reference
[1]
V Ranganayaki Rao, M Y Vishwanath Sastry, M Gururaj and J Vishwanath, A
laboratory manual in Physics, Page-11.
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