Question

(a) Why are the connections between the resistors in a meter bridge made of thick copper strips ?

(b) Why is it generally preferred to obtain the balance point in the middle of the meter bridge wire?

(c) Which material is used for the meter bridge wire and why?

OR

A resistance of R draws current from a potentiometer as shown in the figure. The potentiometer has a total resistance R_{o $straight capital omega$}. A voltage V is supplied to the potentiometer. Derive an expression for the voltage across R when the sliding contact is in the middle of the potentiometer.

Solution

a) The resistivity of copper wire is very low. The connections between the resistors are made of thick wires so as to increase the rate of cross-section. Therefore, the resistance of wires is almost negligible.

b) Balance point is obtained in the middle of the meter bridge wire so as to increase the sensitivity of the meter bridge.

c) Constantan is used for meter bridge wire because its temperature coefficient of resistance is almost negligible due to which the resistance of the wire does not change with increase in temperature of the wire due to flow of current.

OR

Total resistance is given by, R_tot = $straight R subscript straight o over 2 plus straight space fraction numerator straight R subscript 0 over 2. straight R over denominator straight R subscript 0 over 2 plus straight space straight R end fraction$ = $equals space fraction numerator straight R space left parenthesis straight R subscript straight o space plus space 4 straight R right parenthesis over denominator 2 left parenthesis straight R subscript straight o space plus space 2 straight R right parenthesis end fraction$

Total current through the device is given by, I_total= V / R_total

Current through resistance R is given by, I₂ = I_total x $fraction numerator begin display style bevelled straight R subscript straight o over 2 end style over denominator bevelled straight R subscript straight o over 2 space plus space R end fraction$
$space space space space space space equals space straight I subscript total space straight x space fraction numerator straight R subscript straight o over denominator straight R subscript straight o space plus space 2 straight R end fraction space space space space space space equals space fraction numerator straight V.2 space left parenthesis straight R subscript straight o space plus space 2 straight R right parenthesis over denominator straight R space left parenthesis straight R subscript straight o space plus space 4 straight R right parenthesis end fraction straight x fraction numerator straight R subscript straight o over denominator straight R subscript straight o space plus space 2 straight R end fraction straight I subscript 2 space straight R equals space fraction numerator 2 VR subscript straight o over denominator straight R space left parenthesis straight R subscript straight o space plus space 4 straight R right parenthesis end fraction Voltage space across space resistance space is space given space by space straight V comma space straight I subscript 2 straight R space equals space fraction numerator 2 VR subscript straight o over denominator straight R subscript straight o space plus space 4 straight R end fraction$

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