Specific Resistance Of The Material Of A Wire
Current Electricity of Class 12
SPECIFIC RESISTANCE OF THE MATERIAL OF A WIRE USING A METER BRIDGE
A known length (L) of a wire is connected in one of the gaps (P) of a meter bridge, while a Resistance Box is inserted into the other gap (Q). The circuit is completed by using a battery (B), a rheostat (Rh), a key (K) and a galvanometer (G). The balance length (l) is found by closing key K and momentarily connecting the galvanometer until it gives zero deflection (null point). Then, 

(using the expression for the meter bridge at balance.)
Here, P represents the resistance of the wire while Q represents the resistance in the resistance box. The key K is kept open when the circuit is not in use.
The resistance of the wire, P = ⇒ ρ =
where r is the radius of wire and L is the length of the wire, r is measured using a screw gauge while L is measured with a scale.
Errors
The major systematic errors in this experiment are due to the (i) heating effect, (ii) end corrections introduced due to shift of the zero of the scale at A and B, (iii) stray resistances in P and Q, (iv) errors due to non−uniformity of the meter bridge wire.
Error analysis:
End corrections can be estimated by including known resistances P_{1 }and Q_{1 }in the two ends and finding the null point:
(where α and β are the end corrections.)
When the resistance Q1 is placed in the left gap and P1 in the right gap,
which gives two linear equations for finding α and β.
In order that α and β be measured accurately P_{1 }and Q_{1} should be as different from each other as possible.
For the actual balance point, ,
Errors due to non−uniformity of the meter bridge wire can be minimised by interchanging the resistances in the gaps P and Q.
∴, where δl′1 and δl′2 are of the order of the least count of the scale.
The error is, therefore, minimum if l′_{1} = l′2 i.e. when the balance point is in the middle of the bridge. The error in ρ is .
Illustration 13.With two resistances R1 and R2(> R1) in the two gaps of a metre bridge, the balanced point was found to be 1/3m from the zero end. When a 6 Ω resistance is connected in series with the smaller of the two resistances, the point is shifted to 2/3 m from the same end. Calculate R1 and R2.
Solution:, where l is in metre.
or,R_{2 }= 2R_{1} . . . (i)
Again,
or, R_{1} + 6 = 2R_{2} . . . (ii)
From (i) and (ii)
R1 = 2Ω and R2 = 4 Ω.
 Electric Current
 Mechanism Of Current Flow In Metallic Conductors
 Ohm's Law
 Specific Resistance Of The Material Of A Wire
 Measurement Of Unknown Resistance Using A Post Office Box
 Classification Of Materials In Terms Of Conductivity
 Kirchhoff Law
 Grouping Of Resistances
 Grouping Of Identical Cells
 RC−Circuit
 Measuring Instruments
 Verification Of Ohm’s Law Using Voltmeter And Ammeter
 Potentiometer
 Energy, Power And Heating Effect Of The Current
 solved question
 Exercise 1
 Exercise 2