Meter Bridge - Construction, Diagram, Practice problems, FAQs

Measurement plays an important role in physics. Let’s imagine the following scenario:you went to the physics lab, you found four resistors lying on the desk. You looked at three of them, their resistances were written across a label stuck on them, but the value of the fourth resistance is unknown. So how to calculate the value of unknown resistance? Equipment like meter bridges can help us find this out. The Meter Bridge was built by Sir Charles Wheatstone. It was developed from the Wheatstone Bridge, which works on a principle called “bridge balancing” condition. It also carries other names like slide wire bridge or Carey Foster Bridge.

Table of contents

Construction of a meter bridge
Meter bridge derivation
Practice problems
FAQs

Construction of a meter bridge

A meter bridge is used to find the unknown resistance of a resistor. It is based on the balanced wheatstone bridge principle. It has metallic strips for providing electrical contact. A wire having a length of and a uniform cross section is connected end to end. In the region between the strips, resistance boxes and are connected. A jockey is connected from point and is free to slide on the wire The reading on the scale (in for which the unknown resistance shows null deflection in the galvanometer is known as the “balancing length” corresponding to resistance It is noted as Then the balancing length corresponding to the known resistance becomes The jockey is placed on different points of the wire and the balancing lengths corresponding to resistances and are noted. After noting down about readings, the average of the readings gives the value of

Meter bridge derivation

According to the working principle of meter bridge, the resistance is directly proportional to its corresponding balancing length. Let be the balancing length corresponding to the resistance Then is the length corresponding to the resistance

Dividing equations and we get

From the above equation, the value of can be found by cross multiplication.

Practice problems

Q 1. In a meter bridge with a standard resistance of in the right gap, the ratio of balancing lengths is . Find the value of the other resistance.

A. Given

Let be the unknown resistance. Then,

Q 2. In a meter bridge, the value of known resistance in the resistance box is . The balancing length corresponding to unknown resistance is . Calculate the unknown resistance.

(a) (b) (c) (d)

A. a

Let

Q 3. In the following diagram, the meter bridge is balanced. The wire has a resistance of Find the value of the unknown resistance Also calculate the current drawn from the battery ?

A. When the bridge is balanced, null deflection is observed in the galvanometer.

Let

and

Balancing length corresponding to

Now total resistance of the wire

Resistance of the upper portion

Now total resistance of the circuit,

Equivalent resistance

Current drawn from the battery,

Q 4. In the figure shown below, the wire has uniform resistance. The galvanometer shows no deflection when the length is and is If the value of is doubled, what is the percentage change in balancing length?

A. Since the bridge is in balanced condition,

Solving, we get,

Let be the new balancing length when the value of is doubled. Then,

, solving we get

percentage change in balancing length,

FAQs

Q 1. The wire in a meter bridge is made of a material having low temperature coefficient. Why?
A. Low temperature coefficient of the wire would ensure that the resistance of the wire does not change appreciably.

Q 2. Is the meter bridge AC or DC bridge?
A. The meter bridge is a DC bridge.

Q 3. What is the dimensional formula for resistance ?

A.Resistance

Q 4. Can a meter bridge be used to find the internal resistance of a cell?
A. No, a meter bridge can only calculate the value of resistance. Potentiometer is used for finding the internal resistance of a cell.