## Aim/Aim of Experiment

To Find the Resistance of a given wire Using the Metre Bridge and hence Determine the Resistivity (Spacific Resistance) of it’s Material.

## Apparatus/Material Required

- A Metre Bridge (Side wire Bridge)
- A Leclanche Cell (Battery Eliminator)
- A Galvanometer
- A Resistance Box
- A Jocky
- A One-way Key
- A Resistance wire
- A Screw Gauge
- A Meter Scale
- A Set Square
- Connecting wire
- A Piece of Sand Paper.

## Theory

Metre 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:

XR=L(100−L)

(i) The unknown Resistance X is given by

X=(100-L)/LR (Since XR=L(100-L)

Where R is known Resistance placed in the left gap & unknown Resistance X in the Right gap of Metre bridge, L (cm) is the length of Metre bridge wire from zero end upto balance point.

(ii) The Specific Resistance of the Material is given by

ρ=XπD2/4L (Since ρ=πD2XL)

Where L is the length & D is the diameter of the given wire.

## Circuit Diagram

## Procedure

**For Resistance:**

- Arrange the Instruments as shown in the circuit diagram.
- Connect the Resistance wire whose resistance to be determined in the right gap between C and B, Take care that no part of the wire forms a loop
- Connect resistance box of low range in the in the left hand gap between A and B
- Make all other connections as shown in the circuit diagram
- Take out some resistance (say 2 ohms) from the resistance box, plug the Key K.
- Touch the Jockey gently first at left end and then at right end of the bridge wire.
- Note the deflection in the Galvanometer show deflections in opposite directions, the connection are correct. If the deflection is one side only, then there is some fault in the circuit. Check it or Take help your teacher and rectify the fault.
- Move (Slide) the Jockey gently along the wire from left to right till galvanometer given zero deflection. The point where the Jockey is touching the wire is null point D.
- Choose an appropriate value of R from the resistance box such that there is no deflection in the galvanometer when the jockey is the nearly in the middle wire (i.e. between us to 55 cm).
- Note position of point D (with the help of a set square) to know balancing length AD=L.
- Take at least four sets of observation in the same way by changing the value of R in steps.
- Record your observations.

**For Specific Resistance:**

- Cut the Resistance wire at the points where it leaves the terminals, stretch it and find it’s length by using a Meter scale.
- Measure the diameter of the wire at least at four piece, in two matul perpendicular directions at each place with the help of Screw guage.
- Record your observations as given in tables.

## Observations

1. Length of given wire (L) = 56 cm.

2. Table for unknown Resistance (X).

Serial No. of Obs. | Resistance from the Resistance box R (ohm) | Length AB = l (cm) | Length BC = (100-l) (cm) | Unknown Resistance X = [(100-l)/l] (ohm) |
---|---|---|---|---|

1. | 5 | 43.8 | 56.2 | 6.415 |

2. | 10 | 61.5 | 38.5 | 6.260 |

3. | 15 | 70.5 | 29.5 | 6.276 |

4. | 20 | 76.5 | 23.5 | 6.144 |

3. Least Count of the Screw gauge:

- Pitch of Screw gauge= 1 mm.
- Total no. of divisions on the circular scale = 100.
- Least count of given Screw gauge = Pitch/Number of divisions on the circular scale, So Least count = (1/100) = 0.01 mm.
- Zero Error (e) = -12 mm.
- Zero Correction (c) = (-e) = 12 mm.

4. Table for Diameter (D) of the wire:

Serial No. of Obs. | Linear Scale Reading N (mm) | (Circular Scale Reading) No. of Circular Scale Division on reference line (n) | (Circular Scale Reading) Value n × (L.C.) (mm) | Observed Diameter D_{0} = N+n×L.C (mm) | Calculated Diameter D = D_{0}+C (mm) |
---|---|---|---|---|---|

1. | 0 | 21 | 0.21 | 0.21 | 0.33 |

2. | 0 | 24 | 0.24 | 0.24 | 0.36 |

3. | 0 | 23 | 0.23 | 0.23 | 0.35 |

## Calculations

- Calculations for X:
- From position of D, find l cm and write in column 3 of Table 1.
- Find length (100-l) cm and write in column 4.
- Calculate X and write in column 5.
- Mean X = [(X1+X2+X3+X4)/4] = 6.274 ohm.

- Calculation for D:
- Mean corrected diameter = [(D
_{1}+D_{2}+D_{3})/3] = 0.346 mm or 0.035 cm.

- Mean corrected diameter = [(D
- Calculation for (Spacific Resistance) resistivity of wire:
- Spacific resistance of the material of the given wire ρ = πD
^{2}/4L, ρ=[(6.274×3.14×0.035×0.035×10-4)/4×56] = 1.077×10^{-6}ohm-m.

- Spacific resistance of the material of the given wire ρ = πD

## Result

- The value of unknown resistance X = 6.274 ohm.
- The spacific resistance of the material of the given wire = 1.077×10
^{-6}ohm m. - Percentage error = +-5%.

## Precautions

- The connection should be neat, clean and tight.
- Move the jockey gently ever the bridge wire and don’t rub it.
- All the plugs in the Resistance box should be tight.
- The plug in key K should be inserted only when the observations are to be taken.
- Null point should be brought between 45 cm and 55 cm.
- Set square should be used to note null point to avoid error of parallax.
- At one place, diameter of wire should be measured in two mutually perpendicular directions.
- Make sure the wire should not make a loop.

## Sources of Error

- The instruments like Screws guage may be loose.
- The plugs may not be clean.
- The wire may not have uniform thickness.
- The Screw gauge may have faults like back lash error and wrong pitch.
- The wire makes loop.

## Viva Voice Questions with Answers

**Question 1:** Define resistivity or specific resistance of the material of conductor.

**Answer:** (Spacific Resistance) Resistivity is defined as the resistance of a conductor of unit length and unit cross-sectional area. The unit of resistivity is ohm-metre (Ω-m). ρ=RA/l, If l=1mA = 1m2, then ρ=R.

**Question 2:** Define electrical conductivity.

**Answer:** It is reciprocal of resistivity. It is represented by the symbol σ =1/P. The unit of electrical conductivity is Siemen per metre (Sm^{-1}).

**Question 3:** What is the order of magnitude of resistivity of conductors?

**Answer:** Resistivity of the conductors is of the order of 10^{-8} Ω-m.

**Question 4:** Define temperature coefficient of resistance.

**Answer:** Temperature coefficient is defined as the increase in resistance of a conductor of unit resistance due to unit increase in temperature. a = [(R_{2}-R_{1})/R_{1}(t_{2}-t_{1})], If R1=1, t_{2}-t_{1}=1, then a = (R_{2}-R_{1}).

**Question 5:** Why is a large current not allowed to flow the circuit during the experiment.

**Answer:** If large current is passed or passed for a long time then wire become hot and its resistance increases. Therefore, the V-I graph will not be a straight line and Ohm’s law is not valid.

**Question 6:** Can we take a metal wire in place of alloy wire whose resistance is to be measured?

**Answer:** No, Because large current will flow and battery will damage.

**Question 7:** Why is the a meter always connected in series to measure the current?

**Answer:** It is connected in series with circuit in order to measure the current without any change in magnitude.

**Question 8:** Why is the voltmeter is connected in parallel?

**Answer:** So that it can measure the potential drop without any change in its magnitude.

**Class 12 Physics Practicals:**

- To Determine Resistance Per cm of A Given Wire by Plotting A Graph for Potential Difference Versus Current
- To Find The Resistance of A Given Wire using The Metre Bridge and Hence Determine The Resistivity (Spacific Resistance) of It’s Material
- To Verify The Laws of Combination (Parallel) of Resistances using A Metre Bridge
- To Verify The Laws of Combination (Series) of Resistances Using A Metre Bridge
- To Compare The EMF of Two Given Primary Cells Using Potentiometer
- To Determine The Internal Resistance of A Given Primary Cell Using Potentiometer

Bottle me bhar ke ……such a beautiful presentation

Thank you

Nice information.