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Objective:
1. Connecting a simple electric circuit.
2. Measuring an unknown resistance of a metallic wire.
3. Calculating the resistivity of the metallic wire, which characterize
the substance.
4. Introducing different types of resistances to the student.
Apparatus:
1. DC power supply (battery).
2. Meter bridge.
3. Galvanometer with the zero in the middle.
4. Unknown resistance.
5. Rheostat.
6. Resistance box.
7. Micrometer to measure the diameter of the wire.
8. Jockey.
9. Connecting wires.
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Theory:
B I
3
R1
I1
K2
I C
A
I
G
I2
I
R3
IG
R2
R4
D
I4
K1
Figure (1)
The meter bridge theory relies on Wheatston Bridge principal which
consists, as in Figure (1), of four resistors connected along the sides of a
diamond –shape in respcet. The two points C and A are connected to an
electrical current source by the switch K 1 and the points B and D are
connected to a sensitive galvanometer that has the zero in the middle.
When the circuit is closed, the current I is divided at C into I 1 , I 2 and at
the point B I1 is divided into I G , I 3 . At D, the current I G gathers into I 2
so the total is I 4 then I 3 and I 4 gathers at A to become I once again.
Therefore,
I  I1  I 2
I1  I G  I 3
I4  I2  IG
If it is possible to change the value of any resistance in order to have zero
deflection in the galvanometer, then this indicates that the current
between B and D is equal to zero and the potential difference between B
and D is equal to zero. Thus the Bridge is in equilibrium.
At equilibrium we have:
1. Potential of B = potential of D, no current will pass between them.
2. Currents turn into I 1  I 3 and I 4  I 2
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3. Potential differences develop into VCD  VCB and VDA  VBA
i.e,
I1 R1  I 2 R2
(1)
I 3 R3  I 4 R4
(2)
Now dividing equation (1) by equation (2), knowing that I 1  I 3 and
I 4  I 2 , leads to:
R1 R2

R3 R4
(3)
Also,
R1 R3

R2 R4
(4)
So Wheatstone Bridge can be used to find an unknown resistance, for
instance R3 , where the other three resistances are known.
Meter Bridge is the simplest form of the Wheatstone Bridge. As shown in
the circuit diagram below, it consists of a one meter long wire that has a
uniform cross section and the wire is tightened along a wooden ruler. The
resistance of a one meter of the wire is S . The unknown resistance R x ,
which is a wire of length L and cross section A  r 2 , is connected to
one end of the bridge's wire. While the known resistance, which is a
resistance box RB , is connected to the other end. The galvanometer is
connected to a jockey made of copper, that can be moved on the tight
wire to get the equilibrium (zero deflection). Hence:
Rx SL1

RB SL2
(5)
where R x , RB , SL1 and SL 2 represent the resistances R1 , R3 , R 2 and R 4
respectively as in Figure (1).
From the previous equation we conclude that:
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Rx L1

RB L2
(6)
knowing RB , L1 and L2 , you can determine the unknown resistance R x .
If you need to find the resistivity  of the resistor R x we use:

Rx A
L
where:
 is the resistivity of the substance of the wire, measured in   m .
R x is the unknown resistance, measured in  .
L is the length of the unknown wire, measured in m .
A is the cross section of the wire, measured in m 2 .
Precautions:
1. Don't keep the jockey on the meter bridge wire for a long time
(Tap it only).
2. Measure the length L1 from the end connected to the unknown
resistance R x .
Circuit diagram:
G
Procedure:
1. Connect the circuit as shown in figure.
2. Insert an appropriate value of the resistance box RB and set the
length of the wire ( L ) that its resistance to be calculated. Then put
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the jockey at the ends of the bridge's wire and make sure that the
galvanometer deflects in two different directions.
3. Move the jockey on the wire of the bridge until you reach the
equilibrium where the galvanometer reads zero. Record L1 , L2 .
4. Change the value of RB and L , get the equilibrium and record the
new values of L1 and L2 .
5. Repeat the previous step and record your results in Table (1).
6. Plot a graph of R x versus R x and find the slope of the line as in
Figure (2).
7. Measure the diameter of the wire then calculate its cross section.
8. Calculate the resistivity of the wire (that has resistance R x ) using:
  Slope  A
Rx
L
Figure (2)
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Results:
Table (1)
No.
Lm
RB  
L1 m 
L2 m 
R‫ ء‬
RB L1

L2
1
2
3
4
5
6
7
8
9
10
The diameter of the wire:
r  mm  m
The cross section of the wire:
A  r 2  m 2
The slope of the line:
Slope   m
The resistivity of the wire:

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Rx A
 Slope  A    m
L
Questions
Theoretical Questions:
1. What is the relation between the geometric shape and the resistance
of a metallic substance?
2. Define the resistivity. What its unit?
3. What is the difference between the meter bridge and Wheatston
bridge? Why are they used in electric circuits?
Experimental Questions:
1. At the equilibrium point of the circuit explain the zero reading of
the galvanometer?
2. Why were asked not to rub the jockey on the wire of the meter
bridge?
3. What is the aim of plotting the graph of R x versus L ?
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