post office box experiment

Determine Unknown Resistance by a Post Office Box

Experiment: To determine the unknown resistance by a Post Office Box

Theory: By inserting appropriate resistance in the post office box current passing through the galvanometer can be made zero. If the potentials between points B and D are equal i.e., there is no potential difference between the two terminals of a galvanometer, then this phenomenon happens. In this situation, no deflection is found in the galvanometer and the bridge remains in the equilibrium condition. Now according to Wheatstone bridge balanced condition,

S = R x Q/P

If P = 10 ohm and Q = 10 ohm

So, S = (10 x R) / 10 = R ohm

Again by putting P = 100 ohms and Q = 10 ohms, if the experiment is performed then it will be seen,

100/10 = R/S

So, S = 10R/100 = 1/10 R ohm.

Similarly taking P = 1000 ohm and Q = 10 ohms, if the experiment is performed, then we get 1000/10 = R/S

So, S = 1/100 x R ohm … … … (1)

By this instrument, the value of unknown resistance can be determined up to the second digit after the decimal. Here R = resistance of the 3rd arm.

Description of the instrument

A Post Office Box can also be used to measure an unknown resistance. It is a Wheatstone bridge with three arms; while the fourth arm(s) is the unknown resistance. Post office box (in short, PO box) is the special form of Wheatstone bridge. It is called a post office box because it was originally used by the postal department for the measurement of the resistance of the telegraph wires and cables.

Normally, with the help of this instrument, we can measure both low and high resistances. It is composed of some fixed value resistance coils. Coils are arranged in succession and form three arms of the Wheatstone bridge. The experimental unknown resistance S is the fourth arm of the bridge. Like the resistance box, here also coils are in a box. On the top platform of the box, two ends of each coil are connected by solid brass blocks. Brass blocks an arranged in adjacent three rows. Between two successive blocks, there is an arrow-shaped gap. If the plug of the gap is withdrawn fixed resistance is included in the circuit.

In Figure, the schematic diagram of the post office box is shown. In this instrument, three sections of coil resistances of varying magnitudes are connected by plugs and are marked as AC. CD and AE which constitute respectively the three arms P, Q, and R of the Wheatstone bridge. The arms P and Q are called ratio arms. Each of if contains three resistors of 10, 100 and 1000 Ω values connected in series. Third arm R normally consists of resistances from 1 Ω to 5000 Ω connected in series. When the plug of any coil is taken out, its resistance will be included in the circuit. An unknown resistance S is connected between points D and E which forms the fourth arm of the Wheatstone bridge. A battery B is connected between points A and D through a tapping key K 1 and a galvanometer is connected between points C and E through another tapping key K 2 .

The lower portion of the key K 1 and the point A is connected internally. Similarly, point C and the lower portion of the key K 2 is connected internally. So, try the key current in the main point and by the key K 2 current in the galvanometer can be made on and off.

Procedure :

(1) By rubbing the ends of connecting wires and contact points thoroughly connection is made tightly according to the figure.

(ii) From each arm of P and Q, 10-ohm resistance plugs are taken out. Keeping the resistance of the third arm R zero, first the key of the battery circuit K 1 is pressed and then the key K 2 of the galvanometer circuit is pressed and the deflection of the galvanometer is observed. Now withdrawing the ∞ (infinity) plug the deflection of the galvanometer is observed again. In this case, if the deflection of the galvanometer is opposite to the first deflection, then it is considered that the circuit connection is alright.

(iii) Starting from the higher values of resistance of the third arm deflections of the galvanometer are noticed by reducing the value of resistance progressively. When the galvanometer gives zero deflection for P = Q = 10 ohms, the unknown resistance S = R will be equal to the third arm resistance. If the deflection is not made zero, then due to the two successive resistances the deflection will be opposite. In this situation, the value of the unknown resistance S is between these values.

(iv) Now in arm P instead of 10 ohms, 100-ohm resistances are inserted. As before the resistance of the second arm, Q is kept at 10 ohms. So Q/P ratio will be 1/10, hence in balanced condition R = 10 S. Now as before resistance plugs from the third arm R are withdrawn so that galvanometer deflection becomes zero. In this situation, unknown resistance S = R/10.

(v) Similarly, 1000 ohm resistance is inserted in arm P and in Q arm 10-ohm resistance is inserted and the experiment is performed as before.

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What is a post office box in physics?

The post office box was a Wheatstone bridge-style testing device with pegs and spring arms to close electrical circuits and measure properties of the circuit under test.

Table of Contents

Why the instrument is called post office box?

The box containing Wheatstone bridge was used in the United Kingdom by engineers in General Post Office, who used it in UK telecommunications to trace electrical faults. Therefore, for historical reasons it was named “Post office box” as it was carried by post office engineers.

Which metal is used in post office box?

The best material for resistance in post box resistor is Manganin. It is an alloy of copper (85%), Manganese (12%) and Nickel (2%).

What is the aim of the post office box experiment?

Post Office Box is helpful in physics experiment to determine the unknown resistance of wires like Constantan and Nichrome etc. With the help of Nvis 6041, the student can learn the principle of Post Office Box and its working. It can determine the specific resistance of different types of wire.

What is post box explain how does it work?

A post box is a numbered box which are available on rent at certain major post offices. Every post box is allocated a number and only postal articles bearing that number are placed into that box.

What is post office Works explain how does it work?

People mail their letters and packages by placing them in a mailbox or taking them directly to the post office. At the post office, postal workers sort the mail by size. Letters go through a machine that cancels the stamps. This means that the machine prints lines over the stamps so that they cannot be used again.

What is measured by using post office box?

A Post Office Box is used to measure an unknown resistance. It is basically a Wheatstone bridge with three arms known as P, Q, and R; while the fourth arm is the unknown resistance, denoted by S.

What is the formula of meter bridge?

ρ=Lπr2X ; Where L be the length of the wire and r be its radius.

What is Wheatstone bridge principle?

What is the 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.

Can we send clothes through post office?

If a parcel contains cloth or woolen material it must be packed in a strong wrapper with an outer covering of stout card-board or cloth. It is suggested to use a wooden or a stout cardboard case according to the nature of the article for packing a parcel.

Can we send sweets by speed post?

No, you cannot send food items through India Post.

How do I add another person to my P.O. box?

• Ask the clerk at the post office where you have the box for the proper form to add a name to the list of people who get mail at that box.
• Fill in the name and physical address on an empty line on the card that’s handed to you.
• Complete any other required information.

Which is the principle followed in PO box?

D) Principle of wheatstone bridge. Hint: Post office box is a wheatstone bridge style testing device with pegs and spring arms in order to close the electrical circuit to measure the properties of the circuit under test. Basically, a post office box is a measuring device.

What is half deflection method?

The half deflection method is the method by which an internal resistance of a cell can help in evaluating value which is considered as high. The deflection of half is considered as a value obtained along with the cell alone.

How can potentiometer be used to calculate potential difference?

The potentiometer is an instrument used for measuring the unknown voltage by comparing it with the known voltage. It can be used to determine the emf and internal resistance of the given cell and also used to compare the emf of different cells. The comparative method is used by the potentiometer.

Why post box is red in colour?

In early Victorian era the color of post box was Green in Britain. Then during the mid 19th century it was changed to Red. So with the Britishers the color of post box also came to its colonies like India, Australia, etc.

What is the colour of post box?

However, there is some variety indicating uncertainty as to the correct green to be used. Royal Mail have agreed that, only where there is historic precedent, will post boxes be painted in any colour other than the current official, standard colour- red.

When was the post box invented?

Channel Islands Box (1852) The first post box installed by the British Post Office.

What is the main function of post office?

The primary function of Post Office is collection, processing, transmission and delivery of mail.

What is the importance of post office?

Postal services are also valuable to the government of some countries. They use the services to coordinate with other offices- to send notices, memos, and other documents. It is useful especially to places that are hard to reach. They event sent packages and parcels from one post office to another.

How many types of post office are there?

It is basically classified into 3 types, namely – Head Post office, Sub Post Office and Branch Post Office.

Which is more accurate voltmeter or potentiometer?

Potentionmeter measures the potential difference more accurately than a voltmeter, because the potentionmeter.

What is null point in meter bridge?

In a meter bridge experiment, a null point is obtained at 20 cm from one end of the wire when resistance x is balanced against another resistance y. If x

Which wire is used in meter bridge?

In a metre bridge, wires of nichrome, manganin and constantan are used because it has high resistance and low-temperature coefficient of resistance.

Why jockey is used in meter bridge?

The jockey is used to slide on the bridge wire. It is a metal rod with one end as knife edge. Now adjust the value of resistance in the resistance box and slide the jockey along the wire. This process is to be done until the galvanometer shows a zero or null deflection.

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Measurement of an unknown resistance using a Post Office Box

A Post Office Box can also be used to measure an unknown resistance. It is a Wheatstone Bridge with three arms P, Q and R; while the fourth arm(s) is the unknown resistance. P and Q are known as the ratio arms while R is known as the rheostat arm.

 At balance, the unknown resistance

S = (P/Q) R                                                           …… (1)

The ratio arms are first adjusted so that they carry 100 W each. The resistance in the rheostat arm is now adjusted so that the galvanometer deflection is in one direction. If R = R0 (ohm) and R = R0 + 1 (ohm) are the resistance in rheostat arm, for which the deflection in galvanometer is in opposite direction, then it implies that the unknown resistance ‘s’ lies between R0 & (R0 + 1) ohm.

Alt txt: resistance-using-post-office-box

Now, the resistance in P and Q are made 100 W and 1000 W, respectively, and the process is repeated. Equation (1) is used to compute S. The ratio P/Q is progressively made 1:10, and then 1:100. Thus, the resistance S can be accurately measured.  

 The major sources of error are the connecting wires, unclear resistance plugs, change in resistance due to Joule heating, and the insensitivity of the Wheatstone bridge

These errors may be removed by using thick connecting wires, clean plugs, keeping the circuit on for very brief periods (to avoid Joule heating) and calculating the sensitivity.

In order that the sensitivity is maximum, the resistance in the arm P is kept close to the value of the resistance S.

Illustration:

 Resistance of a conductor is 1.72 W at a temperature of 20°C. Find the resistance at 0oC and 100°C. Given the coefficient of resistivity is a = 0.00393/oC.

R = R0 (1 + aDT)

R = 1.72 W (1 + 0.00393) × (0°C – 20°C) = 1.58 W

At T = 100°C

R = 1.72 W [1 + 0.00393) × (100°C – 20°C)] = 2.26 W

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Current Electricity of Class 12

Measurement of unknown resistance using a post office box.

Now, the resistances in P and Q are made 100 Ω and 1000 Ω, respectively, and the process is repeated.

Equation (1) is used to compute S.  The ratio P/Q is progressively made 1:10, and then 1:100. Thus, the resistance S can be accurately measured.

The major sources of error are the connecting wires, unclear resistance plugs, change in resistance due to Joule heating, and the insensitivity of the Wheatstone bridge.

These errors may be removed by using thick connecting wires, clean plugs, keeping the circuit on for very brief periods (to avoid Joule heating) and calculating the sensitivity.

In order that the sensitivity is maximum, the resistance in the arm P is kept close to the value of the resistance S.

Illustration14. In an experiment with a post−office box, the ratio arms are 1000 : 10.  If the value of the third resistance is 999 Ω,. find the unknown resistance.  

Solution: The ratio arms are 1000 : 10 

∴ P/Q = 1000/10 = 100

Third resistance R = 999 Ω

Let x be the unknown resistance. 

We know that,

∴ X = Q/P x R = 1/100 x 999 = 9.99 Ω

Illustration15.When two resistances X and Y are put in the left hand and right hand gaps in a meter bridge,  the null point is at 60 cm. If X is shunted by a resistance equal to half of itself then find the shift in the null point.

⇒I = 33.3 ∴ Shift  = 60 – 33.3 = 26.7 cm

Related Topics

• Ohm's Law
• Kirchhoff Law
• Electric Current
• Mechanism Of Current Flow In Metallic Conductors
• Specific Resistance Of The Material Of A Wire
• Classification Of Materials In Terms Of Conductivity
• Grouping Of Resistances
• Grouping Of Identical Cells
• Measuring Instruments
• Verification Of Ohm’s Law Using Voltmeter And Ammeter
• Potentiometer
• Energy, Power And Heating Effect Of The Current
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Specific Resistance of the Material of a Wire using Meter Bridge and Post Office Box

The resistance of a wire of length l and diameter D is given by \begin{align} R=\frac{\rho l}{A}=\frac{4\rho l }{\pi D^2},\nonumber \end{align} where $\rho$ is resistivity (or specific resistance) of the material of the wire. The unit of resistance R is Ohm ($\Omega$) and that of the resistivity is Ohm-metre ($\Omega\text{-m}$). The resistivity is a material property and it is reciprocal of conductivity.

To find the resistivity of the material of the wire, we need to measure length l by using a scale, diameter D by using a screw gauge , and resistance R by using a metre bridge. The metre bridge works on the principle of balanced Wheatstone bridge.

Metre Bridge Construction

Metre bridge principle, procedural steps.

• Measure the length l of the given wire by using a scale.
• Measure the diameter D of the given wire by using a screw gauge .
• The resistance of the wire is measured by using a metre bridge. Connect the wire in place of the unknown resistance X .
• Connect the circuit. Slide the jockey on the bridge wire AB to find the null position. The null position N should lie close to the mid-point of AB, say between 30 cm and 70 cm. This improves sensitivity of the metre-bridge. Adjust the known resistance R to do so. Measure the length $l_1$. Reapeat this for five different values of known resistance R .
• Interchange the positions of X and R and repeat steps (4). This takes care of unknown resistances offered by the terminals.
• Calculate mean value of X obtained in steps (4) and (5). Use this to calculate resistivity of the wire.
• Do error analysis to find error in the resistivity.

Questions on Metre Bridge

Question 1: In a metre bridge experiment, it is recommended to have known and unknown resistances of the similar values. This recommendation A. reduces error in finding position of the null point. B. makes null point to lie in the middle of the wire. C. improves sensitivity of the galvanometer. D. reduces current through the galvanometer.

Question 2: In a metre bridge experiment, two students have identical setup and follow similar procedure. But one of the student uses very low source voltage V . This student gets more error because A. it reduces sensitivity of the galvanometer. B. it increases error in position of the null point. C. it increases temperature of the wire. D. it reduces current in the wire.

Question 3: In a modified metre bridge, the length of the bridge wire is reduced to 50 cm from 100 cm. This will A. decrease the error in finding the null point. B. increase the error in finding the null point.

Question 4: In a metre bridge experiment, the known and the unknown resistances are interchanged to remove A. index error. B. end correction error. C. error due to temperature effect. D. random error.

Question 5: The bridge wire in metre bridge construction is made of materials like constantan or manganin because A. they have small resistivity and small temperature coefficient of resistivity. B. they have large resistivity and large temperature coefficient of resistivity. C. they have small resistivity and small temperature coefficient of resistivity. D. they have large resistivity and small temperature coefficient of resistivity.

Solved Problems on Metre Bridge

Problem from iit jee 2014.

• $60\pm0.15\;\Omega$
• $135\pm0.56\;\Omega$
• $60\pm0.25\;\Omega$
• $135\pm0.23\;\Omega$

Solution: Let $\lambda$ be resistance per unit length (in ohm/cm) of the potentiometer wire. Total length of the wire is 100 cm and null point is obtained at $x=40\;\mathrm{cm}$. The resistances of four branches of Wheatstone bridge are, $R_1=R$, $R_2=90\;\Omega$, $R_3=\lambda x$, and $R_4=\lambda(100-x)$. The Wheatstone bridge is balanced if, \begin{align} &\frac{R_1}{R_2}=\frac{R_3}{R_4}, & &\text{or} & & \frac{R}{90}=\frac{x}{100-x}. \end{align} Solve to get $R=60\;\Omega$.

The least count of scale gives error in measurement of $x$, i.e., $\Delta x=0.1\;\mathrm{cm}$. To find error in $R$, differentiate above equation and simplify to get, \begin{alignat}{2} &\frac{\Delta R}{R}=\frac{\Delta x}{x}+\frac{\Delta x}{100-x}. \end{alignat} Substitute values and then solve to get $\Delta R=0.25\;\Omega$.

Problem from IIT JEE 2011

• $10.2\;\Omega$
• $10.6\;\Omega$
• $11.1\;\Omega$

Problem from IIT JEE 2008

Statement 1: In a metre bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.

Statement 2: Resistance of a metal increase with increase in temperature.

• Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1.
• Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.
• Statement 1 is true, statement 2 is false.
• Statement 1 is false, statement 2 is true.

Problem from IIT JEE 2007

• $3\;\Omega$
• $4\;\Omega$
• $5\;\Omega$
• $6\;\Omega$

Problem from IIT JEE 2004

• $B_1$ and $C_1$

Problem from IIT JEE 2003

Solution: If radius of the wire AB is doubled then its resistance ($R=\rho l/A$) becomes one fourth and current ($i=V/R$) becomes four times. However, the potential drop per unit length, $V/l$, remains same.

Problem from IIT JEE 2002

• Are there positive and negative terminals on the galvanometer?
• Copy the figure in your answer book and show the battery and the galvanometer (with jockey) connected at appropriate points.
• After appropriate connections are made, it is found that no deflection takes place in the galvanometer when the sliding jockey touches the wire at a distance of 60 cm from A . Obtain the value of the resistance $X$.
• Screw Gauge - Principle | Problems
• Significant Figures - Rules | Problems
• Measurement error analysis
• Verification of Ohm's law using voltmeter and ammeter

References and External Links

• Concepts of Physics Part 2 by HC Verma (Link to Amazon)
• NCERT User Manual for Experiments (pdf)
• Metre Bridge Experiment on Amrita-CDAC Olabs