Physics

Project
Aim
To study the variation of resistance with length, area of
cross section & material of a wire using a meter bridge.

Apparatus Required
Meter bridge, a wire about 1m long (of material whose specific
resistance is to be determined), a resistance box, a rheostat,
galvanometer, a jockey, one-way key, a cell or battery eliminator,
thick connecting wires, sand paper,
screw gauge.

Theory
Ohm’s Law
“ Ohm’s law states that the voltage across a conductor is
directly proportional to the current flowing through it, provided
all physical conditions and temperatures remain constant.
Mathematically, this current-voltage relationship is written as,

In the equation, the constant of proportionality, R, is called Resistance and has units of ohms, with
the symbol Ω.
The same formula can be rewritten in order to calculate the current and resistance respectively as
follows:

If I is the electric current flowing through a conductor maintain ed at a

potential difference V, According to Ohm’s law,
I proportional to V OR V proportional to I i. e, V= IR
Where R is a constant known as the resistance of a conductor.
The graph connecting I and V is a straight line.
If the temperature changes then Ohm’s law does not hold good because
the resistance R of a conductor with rise of temperature.
Factors on which the resistance of a
conductor depends:

Factors on which the resistance of a conductor

depends:
(1) Length l of the conductor.
{R proportional to I}
(2) Area of cross section a of the conductor.
{R proportional to 1/a}
(3) Temperature t of the conductor
{The resistance of a conductor increases with
rise in temperature. But for semi conductors like
Ge, Si, etc. The resistance decreases with rise in
temperature}.
(4) Material of the conductor
Method to find resistance from Ohm's
law graph
1. Initially, the key K is closed and the rheostat is
adjusted to get the minimum reading in
ammeter A and voltmeter V.
2. The current in the circuit is increased gradually
by moving the sliding terminal of the rheostat.
During the process, the current flowing in the
circuit and the corresponding value of potential
difference across the resistance wire R are
recorded.
3. This way different sets of values of voltage and
current are obtained.
4. For each set of values of V and I, the ratio of V/I
is calculated.
5. When you calculate the ratio V/I for each case,
you will come to notice that it is almost the
same. So V/I = R, which is a constant.
6. Plot a graph of the current against the potential
difference, it will be a straight line. This shows
that the current is proportional to the potential
difference.

Relation Between Resistance And

Length
 The mathematical expression ? = RL can be
rearranged in terms of resistance and length.
In terms of resistance, the above expression
can be given as,R = ? Where,? →
Proportionality constant Removing the
proportionality constant, the expression can
be expressed as,R ∝ LThis. means that the
resistance of a conductor is directly
proportional to the length of that conductor.
Thus, when the length of a conductor is
increased, its resistance increases. And when
the length of conductor is decreased, its
resistance decreases.

Proof of Relation Between Resistance

And Length
Assume that there are two conductors of length L
and cross-sectional area A respectively.
When the potential difference is applied across one
of these conductors, a current flows through
it. Ohm’s law will give the exact equation of this
relationship.
R = VI …(1)
Where,
• R → Resistance
• V → Voltage applied across the conductor
• I → Current flowing through the conductor
If two conductors are joined from end to end, the
total length of the conductor becomes 2L and the
cross-sectional area remains the same i. e, l a

Resistance and Length

Thus, the current flowing through the conductor of
length 2L on the application of voltage V is I/2.
Applying ohm's law,
R' = VI/2
R' = 2VI…(2)
Comparing equations (1) and (2),
R' = 2R
When the length of the conductor is doubled, the
resistance also doubles. This proves that resistance
is directly proportional to length.
Relation Between Resistance and Area
of Cross Section

Resistance: Resistance of a wire is directly

proportional to the length of the conductor and
inversely proportional to the area of the cross-
section.
That is, R∝L/A
Introducing a constant of proportionality,
R=pL/A(where p is the resistivity of the
material.)
 1. From the formula, we can observe that the
resistance is inversely proportional to the
cross-section area.
2. Hence, the resistance increases as the
cross-section area decreases and vice-
versa.

Meter Bridge

• Meter Bridge: A meter bridge, also known as a slide wire

bridge, is a device that works on the Wheatstone bridge idea.
A meter bridge is used to find the unknown resistance of a
conductor. In Physics, while theory forms the basis of our
knowledge, practical’s form our understanding. What is this
device? This is a meter bridge! It consists of a wire of one
meter, which is why it is called a ‘meter bridge’. It is used to
measure the resistance of wires, coils or any other
material. Please read on to learn about the meter bridge
formula, meter bridge diagram, and more.
• In this article, we will provide you with all information about
the meter Bridge, the principle of the meter bridge, meter
bridge experiment class 12 etc. continue to learn the concept
 thoroughly and make no mistakes while answering questions
on the meter bridge.
A meter bridge is an electrical apparatus using which we can
measure the value of unknown resistance. It is made using a
meter long wire of uniform cross-section. This wire is either
nichrome or manganic or constantan because they offer high
resistance and low-temperature coefficient of resistance.
A meter bridge or Slide wire bridge is designed from a
Wheatstone bridge. It is the most basic and functional application
of a Wheatstone bridge.

The principle of Meter bridge

A meter bridge works on the principle of a Wheatstone bridge. A

Wheatstone bridge is based on the principle of null deflection, i.e.
when the ratio of resistances in the two arms is equal, no current
will flow through the middle arm of the circuit. Consider the
diagram of the Wheatstone bridge as shown below. It consists of
four resistances P,Q,Rand S with a battery of EMF E.
 In the balanced condition,
no current flows through the galvanometer, and terminals, B
and D are at the same potential. This condition arises
when, PQ=RS=E Kc.
The Construction of a Meter bridge
1. A meter bridge has a 1m1m long wire of uniform cross-
section area, which is stretched tight.
2. Between two metal strips that are bent at right angles, this
wire is then carefully clamped, as shown in the diagram
below:
3. Within the gap between the metal stripes, resistances are
connected. In the first gap, R, a resistance box, and in the
second gap, a small resistor wire S is connected.
4. The endpoints within which the wire is clamped are
connected to a key through the cell.
5. A galvanometer is connected to the metallic right in the
middle of the two gaps.
6. A jockey is connected at the other end of the galvanometer
(Here, a jockey is a metal rod with a knife-like edge at one
end that slides over the potentiometer wire to make an
electrical connection). The jockey is slid over the meter
bridge wire till the galvanometer shows zero deflection.
 Meter bridge Experiment
Equipment Required
1. Meter Bridge
2. Galvanometer
3. Connecting wires
4. Unknown resistance
5. Resistance Box
6. Jockey
7. One-way key
8. Screw Gauge
9. Lechlanche cell

Procedure
1. Collect all the required instruments and make all the necessary
connections, as demonstrated in the above figure.
2. Take some appropriate kind of resistance out from the
resistance box ‘R’.
3. Now, place the jockey at point A; look that there is a deflection
within the galvanometer. When the jockey is moved from point A
to Point C, the deflection of the galvanometer must go from one
side to the other side. If it is not observed, adjust the known
resistance value.
4. Start sliding the jockey from A towards C and obtain the point
where the deflection of the galvanometer is zero.
5. Proceed with the above strategy for various values of the ‘R’.
Note probably around 5−10 readings.
6. The point where the galvanometer gives null deflection is the
balance point of the meter bridge for the given unknown
resistance.
7. Measure the distance between point A and the balance point of
a given wire using an ordinary meter scale and the radius of the
wire using a screw gauge (Take at least five readings for both the
quantities).
8. Compute the mean value of the unknown resistances obtained
above. It will be equal to the sum of all the values of resistance
divided by the total number of readings taken.
Errors in the Meter Bridge
The most common error that can affect the measurement
accuracy of a meter bridge is the end error. The end error can
come up due to the following reasons:

1. We know that along the length of the bridge wire, a scale is

provided. If the zero of the scale does not coincide with the
starting point of the bridge wire, the 100cm100cm mark on
the scale will not coincide with the endpoint of the wire. This
will lead to incorrect measurements of the balancing length.
2. The non-uniformity of the metal wire might lead to the
generation of stray resistance, and it will create an end error.
We can minimize end error by taking multiple readings of the
experiment by interchanging the unknown and known resistance
in the circuit and by calculating the final value of resistance by
taking the mean of all the observations.

Meter bridge Working

1. To begin with, move the jockey to the endpoints of the wire,
i.e., A and C. The deflection of the galvanometer should be
opposite on both ends.
2. From side A, start sliding the jockey slowly over the wire and
carefully observe where the deflection of the galvanometer
comes out to be zero.
3. If such a point is not obtained, try varying the resistance
across the bridge by changing the resistance on the variable
resistance.
4. Slide the jockey over the wire and carefully observe the point
on the wire where the deflection of the galvanometer comes
out to be zero. This is the null point as represented by the
point ‘B in the diagram.
5. Obtain the length of the null point using the meter scale
attached along the wire. This is the ‘balancing length’ of the
meter bridge.
6. Let the distance between points A and B be ‘L1’
7. Let the distance between points B and C be ‘L2'
where L2=100–L1.
When the galvanometer shows null deflection, the meter bridge
behaves like a Wheatstone bridge and can be represented as:
Advantage of Meter bridge to measure
Resistance
Meter bridge works on principle of wheat stone bridge.
The Wheatstone bridge method is more accurate thanthe
other methods of measuring resistances because it uses
null method. Hence the internal resistance of the cell and
resistance of galvanometer do not affect the null point.

Wheatstone Bridge
Wheatstone bridge, also known as the resistance bridge,
calculates the unknown resistance by balancing two legs
of the bridge circuit. One leg includes the component of
unknown resistance.
The Wheatstone Bridge Circuit comprises two known
resistors, one unknown resistor and one variable resistor
connected in the form of a bridge. This bridge is very
reliable as it gives accurate measurements.

Construction of Wheatstone Bridge

A Wheatstone bridge circuit consists of four arms, of
which two arms consist of known resistances while the
other two arms consist of an unknown resistance and a
variable resistance. The circuit also consists of a
galvanometer and an electromotive force source. The emf
source is attached between points a and b while the
galvanometer is connected between points c and d. The
current that flows through the galvanometer depends on
its potential difference.

Wheatstone Bridge Principle

The Wheatstone bridge works on the principle of null
deflection, i.e. the ratio of their resistances is equal, and
no current flows through the circuit. Under normal
conditions, the bridge is in an unbalanced condition where
current flows through the galvanometer. The bridge is said
to be balanced when no current flows through the
galvanometer. This condition can be achieved by adjusting
the known resistance and variable resistance.

Wheatstone Bridge Derivation

The current through the galvanometer, at the balanced
condition of the bridge, is zero, which is IG = 0. Current
through arms AB and BC is denoted by I1 Current through
arms of AD as well as DC is I2 As per the circuital law of
Kirchhoff, voltage drop through the closed-loop is 0. The
application of this law in the ABDA loop results in the
dropping of the sum of voltage through the individual arms
of the loop which is 0.

I 1P - I 2R = 0
I1/I2 = R/P
Applying Kirchhoff’s law to the loop CBDC
I 1Q - I 2S = 0
I1/I2 = S/Q
Comparing conditions,
R/P = S/Q
P/Q = R/S

This is the formula for Wheatstone Bridge.

Applications of Wheatstone Bridge

• The Wheatstone bridge is used for the precise

measurement of low resistance.
• Wheatstone bridge and an operational amplifier are
used to measure physical parameters such as
temperature, light, and strain.
 • Quantities such as impedance, inductance, and
capacitance can be measured using variations on the
Wheatstone bridge.

Resistance of a given wire by Meter

bridge
Meter bridge apparatus is also known as a slide wire
bridge. It is fixed on the wooden block and consists of a
long wire with a uniform cross-sectional area. It has two
gaps formed using thick metal strips to make the
Wheatstone’s bridge.
Then according to Wheatstone’s principle, we have:
X/R = l/(100-1)
The unknown resistance can be calculated as:
X = R l/(100-l)
Then the specific resistance of the material of the is
calculated as:
P = pie r2 X/L
Where,
• L is the length of the wire
• r is the radius of the wire
Resistance measured in Meter bridge
In meter bridge experiment, it is assumed that the resistance
of the L shaped plate is negligible, but actually it is not so.
The error created due to this is called, end error. To removed
this the resistance box and the unknown resistance must be
interchanged and then the mean reading must be take.

Observations

Table for unknown resistance(X):

S Reading of Balancing X=R(100-l)/l
No. resistance length(l) Ohm
box(R) Ohm cm
1
2
3
4
5

Mean resistance(X)=
Table for mean diameter of the wire(d):
L. C of Screwguage = cm
Zero correction =
SI. PSR HSR Corrected Total Mean
No. HSR (PSR×HSR×LC) Diameter
(d)
cm
1
2
3
4
5

Graph
Relation Between Resistance & Length:
Relation Between Resistance & Radius(Area):

Material of the wires:-

S. Material Resistance Null R=S×I1/100-I1
No of the S (in ohm) point
wire I1 (in
cm)
(1)
(2)
(3)
(4)
(5)
Length of the wire:-
S. No Length Resistance Null R=S×I1/100-
of the S (in ohm) point I1
wire I1(in
(in cm) cm)
(1)
(2)
(3)
(4)
(5)

Area of cross section of the wire:-

S. No Area of Resistance Null point I1 R=S×l1/100-
cross S(in ohm) (in cm) I1
section of
the wire

(1)
(2)
(3)
(4)
(5)

Summary
A meter bridge is an electrical apparatus using which we can
measure the value of unknown resistance. It is made using a
meter long wire of uniform cross-section. This wire is either
nichrome or manganin or constantan. The principle of working of
a meter bridge is the same as the principle of a Wheatstone
bridge. A Wheatstone bridge is based on the principle of null
deflection. Thus, the unknown resistance, S=(100–l1)Rl1.=(100–
1)1.