using the principle of wheat stone bridge describe the method to determine the specific resistance of a wire in a laboratory . draw the circuit diagram and write the formula used
Answers
Metre Brdige:Special Case of Wheat of Whearstone Bridge.
It is a potential device based on the principle of Wheatstone bridge to determine the unknown resistance of a wire.
If ratio of arms resistors in Wheatstone bridge is constant,then no current flows through the galvanometer (or bridge wire.)
Construction: It consists of a uniform 1 metre long wire AC of constantan or manganin fixed along a scale on a wooden base.The ends A anc C of wire are joined to two L shaped copper strips carrying screws as shown.In between these copper strips,there is a third straight copper strip having three connecting screws.The middle screw D is connected to a sensitive galvanometer.The other terminal of galvanometer is connected to a sliding jockey B. The jockey can be made to move anywhere parallel to wire AC.
Circuit: To find the unknown resistance S, the circuit is complete as shown in figure.The unknown resistance wire of resistance S is connected across the gap between points C and D and a resistance box is connected across the gap between the points A and D. A cell , a rheostat and a key (k) is connected between the points A and C by means of connecting screws. In the experiment when the sliding jockey touches the wire AC at any point, then the wire is divided into two parts.These two parts AB and BC act as the resistances P and Q of the Wheatstone bridge.In this way the resistances of arms AB,BC,AD and DC form the resistances P,Q,R and S of Wheatstobe bridge.Thus the circuit of metre bridge is the same as that of Wheatstoe bride.
Method :To determine the unknown resistance, first of all key K is closed and a resistance R is taken out from resistance box in such a way that on pressing jockey B at end points A and C, the deflection in galvanometer is on both the sides.Now jockey is slided on wire at such a position that on pressing the jockey on the wire at that point, there is no deflection in the galvanometer G.In this position, the points B and D are at the same potential;therefore the bridge is balanced.The point B is called the null point.The length of both parts AB and BC of the wire are read on the scale.The condition of balance of Wheatstone bridge is
Q
P
=
S
R
⇒ Unknown resistance,
S=(
P
Q
)R.....................(i)
To Determine Specific Resistance:
If r is the resistance per cm length of wire AC and 1 cm is the length of wire AB,then length of wire BC will be (100-1)cm
∴ P=resistance of wire AB=lr
Q=resistance of wire BC=(100-l)r
Substituting these values in equation (i),we get
S=
lr
(100−l)r
×R or %S=
l
100−l
R...........(ii)
As the resistance (R) of wire (AB) is known,the resistance S may be calculated.
A number of observations are taken for different resistances taken in resistance box and S is calculated each time and the mean value of S is found.
Specific resistance $$p=\dfrac{SA}{l}=\dfrac{S\pi r^2}{L}
$$
Knowing resistance S,radius r by screw gauge and length of wire L by metre scale, the value of p may be calculated.
If a small resistance is to be measured,all other resistances used in the circuit,including the galvanometer ,should be low to ensure sensitivity of the bridge.Also the resistance of thick copper strips and connecting wires (end resistances) become comparable to the resistance to be measured.This results in large error in measurement.
Precautions:
i) In this experiment the resistances of the copper strips and connecting screws have not been taken into account.These resistances are called end-resistances.Therefore very small resistances cannot to be found accurately by Metre Bridge.The resistance S should not be very small.
ii) The current should not flow in the metre bridge wire for a long time, otherwise the wire will become hot and its resistance will be changed.
iii) The resistivity of copper is several times less than the resistivity of the experimental alloy wire.As such area of thick copper strips is more,so strips almost offer zero resistance in the circuit.
iv) If any one resistance in wheat stone bridge is either very small (or very large) in respect of other, then balance point might be very close to terminal A or terminal B.So generally balance point is taken in the middle of the bridge wire,
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