The document provides a detailed explanation of the Wheatstone Bridge, its construction, formula, and principles, focusing on its application for measuring resistances. It outlines the derivation of the bridge's balanced condition and discusses limitations, including issues with lead resistance and the effects of heating. Additionally, it introduces the Meter Bridge, a practical application of the Wheatstone Bridge, detailing its use in determining unknown resistances and providing a methodology for experiments.

1. Wheatstone bridge and application
• Presented by
• Vasudev Shrivastava
• P.G.T.(Physics)
• J.N.V. Nowgong
• District Chhatarpur (M.P.)

2. Wheatstone Bridge
• Scientists use many skills to investigate the world
around them. They make observations and gather
information from their senses. Some observations are
as simple as figuring out the texture and colour of an
object. However, if scientists want to know more
about a substance they may need to take
measurements. Measurement is one of the important
aspects of science. It is difficult to conduct
experiments and form theories without the ability to
measure.
• https://voutu.be/-PhSRUUo Ec

3. Construction of Wheatstone Bridge
• A Wheatstone bridge circuit consists of four arms
of which two arms consists 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 c while the
galvanometer is connected between the points b
and d. The current that flows through the
galvanometer depends on the potential
difference across it.

4. Wheatstone Bridge Formula and
principle
https://youtu.be/3rOvQ3qFZpI
Where, Following is the
formula used for Wheatstone
bridge: P /Q =R/S
• R is the unknown resistance
• S is the standard arm of the
bridge
• P and Q is the ratio of arm of
bridge

5. Wheatstone Bridge Derivation

6. Derivation of condition for balance
bridge
• The current enters the galvanometer and divides into two equal magnitude
currents as I1 and I2. The following condition exists when the current through a
galvanometer is zero,
• I1P=I2R -------------------- (1)
• The currents in the bridge, in a balanced condition, is expressed as follows:
• I1=I3=E/(P+Q ) I2=I4=E/(R+S)
• Here, E is the emf of the battery.
• By substituting the value of I1 and I2 in equation (1), we get
• PE/P+Q=RE/R+S P/(P+Q)=R/(R+S)
• P(R+S)=R(P+Q)
• PR+PS=RP+RQ
• PS=RQ P/Q= R/S -----------------(2)
• R=(P/Q)×S ------------------ (3)
• Equation (2) shows the balanced condition of the bridge while (3) determines the
value of the unknown resistance.
• In the figure, R is the unknown resistance, and the S is the standard arm of the
bridge and the P and Q are the ratio arm of the bridge.

7. Wheatstone Bridge Application
• The Wheatstone bridge is used for the precise
measurement of low resistance.
• Wheatstone bridge along with operational
amplifier is 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.

8. Wheatstone Bridge Limitations
• For low resistance measurement, the resistance
of the leads and contacts becomes significant and
introduces an error.
• For high resistance measurement, the
measurement presented by the bridge is so large
that the galvanometer is insensitive to imbalance.
• The other drawback is the change in the
resistance due to the heating effect of the current
through the resistance. Excessive current may
even cause a permanent change in the value of
resistance.

9. Meter Bridge
https://youtu.be/kwCm_CH5dAA
• A meter bridge also
called a slide wire
bridge is an instrument
that works on the
principle of a
Wheatstone bridge. A
meter bridge is used in
finding the unknown
resistance of a
conductor as that of in
a Wheatstone bridge.

10. How Is A Meter Bridge Used In Finding The Unknown
Resistance?
A meter bridge is an apparatus utilized in finding the unknown
resistance of a coil. The below figure 01& 02 is the diagram of a
useful meter bridge instrument

11. Expression for determine unknown
resistance and resistivity by meter
bridge• In the above figure, R is called as the Resistance, P is the Resistance coming across AB, S is the
Unknown Resistance, Q is the Resistance between the joints BD.
• AC is the long wire measuring 1m in length and it is made of constantan or manganin having a
uniform area of the cross-section Such that L1 + L2 = 100
• Assuming that L1 = L => L2 = 100 – L , Such that P=kL and Q= k(100-L)
• P/Q = R/S
• Relation obtains the unknown resistance ‘S’ of the given wire:
S = RL2/L1 = R(100 – L)/L => S= R(100-L)/L
• We know that S = pl/A => p = SA/l
• And the specific resistance of the material for a given wire is obtained by the relation = => ∏ r2 S/l
• where, r = the radius of the cable and also l = length of the wire.
• In the meter bridge, one of the lateral kinds of resistances is replaced by a wire having a length of
the uniform cross section of about 1m. The other pair consists of one known and an unknown pair
of resistances. The one part of the galvanometer is connected in between both resistances,
whereas the other part of the wire is finding the null point where the galvanometer is not showing
any deflection. At this point, the bridge is said to be balanced.

12. Procedure For Finding The Unknown
Resistance Using Meter Bridge
• Collect the instruments and prepare connections as shown in the above
figure.
• Take some suitable kind of resistance ‘R’ from the resistance box.
• Touch jockey at the point A; look that there exists a deflection in
galvanometer on one of the sides, then contact the jockey on point C of
wire, then the deflection in galvanometer has to be on another side.
• Find the position of the null point having deflection in the galvanometer
that becomes zero. Note the length AB (l) BC = (100 – l).
• Continue the above method for some different values of the ‘R’. Note at
least some 5 readings.
• Consider the point where galvanometer shows a 0 deflection; this is
called balance point.
• Now, Measure the length of given wire by the use of ordinary scale and
radius of the wire by the utilization of a screw gauge, (Take at least five
readings).
• Calculate Mean Resistance of Single Unknown Resistance = Total Sum of
resistances of Unknown resistance from the above five readings)/5.
•

13. Problems Related with Meter Bridge
• Q1. In a meter bridge, there are two unknown
resistance R1 and R2. Find the ratio of R1 and R2
if the galvanometer shows a null deflection at
30 cm from one end?

14. • Q2. In the meter bridge, the null deflection is shown on the galvanometer
which is at a distance of 30 cm from one point. When a known resistance
of 10 Ω is connected in parallel with another unknown resistance S the
null deflection shows at 50 cm from the same point. Find the unknown
resistance of R and S.
• Solution:
• In the first case L1 = 30 cm
• As the resistors are connected in parallel we know that the
equivalent resistance is R1 R2 / R1 + R2
• = 10 * S / 10 + S
• In the second case L1 = 50 cm So L2 = 100 – 50 = 50
• So according to the formula
• R / S = 1
• = R / (10 S / 10 + S) = 1
• So R = 10 S / 10 + S
• Substituting the value of R in equation 1we get

16. Q03 In a meter bridge, the value of resistance in the resistance box is 10 Ω.
The balancing length is l1 = 55 cm. Find the value of unknown resistance.
.

17. Home Assignment
• Q 01 (i) State the principle of working of a meter bridge. (ii) In a meter bridge
balance point is found at a distance l1 with resistance R and S as shown in the
figure. When an unknown resistance X is connected in parallel with the resistance
S, the balance point shifts to a distance l2. Find the expression for X in terms of l1,
l2 and S.

18. Q 02 The four arms of a Wheatstone bridge ( as per following Fig) have the following
resistances : AB = 100Ω, BC = 10Ω, CD = 5Ω, and DA = 60Ω. A galvanometer of 15Ω
resistance is connected across BD. Calculate the current through the galvanometer
when a potential difference of 10 V is maintained across AC.

19. Q.03 In a metre bridge (Fig.), the null point is found at a distance
of 33.7 cm from A. If now a resistance of 12Ω is connected in
parallel with S, the null point occurs at 51.9 cm. Determine the
values of R and S.

20. • Q04 (a) In a metre bridge [Fig. of Q.03], the
balance point is found to be at39.5 cm from the
end A, when the resistor Y is of 12.5 Ω.
Determine the resistance of X. Why are the
connections between resistors in a Wheatstone
or meter bridge made of thick copper strips?(b)
Determine the balance point of the bridge above
if X and Y are interchanged.(c) What happens if
the galvanometer and cell are interchanged at
the balance point of the bridge? Would the
galvanometer show any current?