# Determining Resistance and Resistivity Using a Meter Bridge

## To Find Resistance of a Given Wire Using Meter Bridge and to Determine the Resistivity of its Material

**Table of Contents:**

- Aim
- Materials Required
- Theory
- Circuit Diagram
- Observations
- Calculations
- Result
- Precautions
- Sources of Error
- Viva Questions

## Aim

To find the resistance of a given wire using a meter bridge and hence determine the resistivity (specific resistance) of its material.

## Materials Required

- A meter bridge
- A Leclanche cell (battery eliminator)
- A galvanometer
- A resistance box
- A jockey
- A one-way key
- A resistance wire
- A screw gauge
- A meter scale
- A set square
- Connecting wires
- A piece of sandpaper

## Theory

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:

**
**

The unknown resistance can be calculated as:

**
**

Then the specific resistance of the material is calculated as:

Where,

- L is the length of the wire
- r is the radius of the wire

## Circuit Diagram

## Procedure

- The arrangement of the apparatus should be as shown in the circuit diagram.
- The wire whose resistance is to be determined should be connected in the right gap between C and B without any formation of loops.
- The resistance box should be connected in the left gap between A and B.
- All the other connections should be as shown in the circuit diagram.
- Plug the key K in place of 2-ohm resistance in the resistance box.
- The jockey should be first touched gently to the left end and then to the right end of the bridge.
- The deflections in the galvanometer should be in opposite directions and if it is in one direction then the circuit connections are not correct. Note the galvanometer deflection.
- Let D be the null point where the jockey is touching the wire. The movement of the jockey should be gentle from left to the right of the galvanometer.
- Take a 12 value from the resistance box should be taken such that when the jockey is nearly in the middle of the wire, there shouldn’t be any deflection.
- Note the position of D to know the length of AD = l.
- Four sets of observations should be taken by changing the value of 12.
- Record the observations in a tabular form.
- Stretch the resistance wire to find its length using a meter scale.
- Using a screw gauge, measure the diameter of the wire at four different places keeping it in a mutually perpendicular direction.
- Record the observations in the table.

## Observations

Length of given wire L = …….cm

**Table for unknown resistance (X)**

**Least count of the screw gauge**

Pitch of screw gauge = …….mm

Total no. of divisions on the circular scale = ………..

∴ L.C of the given screw gauge =

= ……mm

Zero error e = ……mm

Zero correction c = -e = ……mm

**Radius of the resistance wire**

## Calculations

**Calculation for X**

The value of l is determined from the position of D and recorded in column 3 of Table 1.

Find length (100 – l) cm and write in column 4.

Calculate X and write in column 5,

**Calculation for D**

Mean corrected diameter =

**Calculation for specific resistance**

Specific resistance of the material of the given wire,

Standard value of the specific resistance of the material of the given wire,

ϱ_{0} = …..ohm.m

Percentage error =

= ………%

## Result

- The value of unknown resistance X = …….
- The specific resistance of the material of the given wire = ………
- Percentage error = …….

## Precautions

- The connections should be neat, tight, and clean.
- Plugs should be tightly connected in the resistance box.
- The movement of the jockey should be gentle and it shouldn’t be rubbed.
- The key K should be inserted only when the observations are to be taken.
- The null point should be between 45cm and 55cm.
- To avoid the error of parallax, the set square should be used to note the null point.
- There shouldn’t be any loops in the wire.
- The diameter of the wire should be measured in two perpendicular directions that are mutual.

## Sources of Error

- The screws of the instrument might be loose.
- The wire might be of non-uniform diameter.
- There might be a backlash error in the screw gauge.

## Viva Questions

**Q1. Why is the meter bridge called so?**

**Ans: **It is called a meter bridge because the bridge uses a one-meter long wire.

**Q2. What is the null point?**

**Ans: **Null point is defined as the point at which a galvanometer reads 0 deflections.

**Q3. Why is the bridge method better than the Ohms law of measurement?**

**Ans: **The bridge method is better than the Ohms law of measurement because of the null method.

**Q4. What is the range of measurement of resistance using a Wheatstone bridge?**

**Ans: **The resistance measurement range using a Wheatstone bridge is between 1Ω to a few megaohms.

**Q5. How can a Wheatstone bridge be used for the measurement of physical parameters?**

**Ans: **A Wheatstone bridge is used to measure physical parameters like temperature, light, etc., using an operational amplifier and rectifiers are used for the conversion of A.C to D.C.