current-electricity Question 55
Question: Q. 9. With the help of the circuit diagram, explain the working principle of metre bridge. How is it used to determine the unknown resistance of a given wire? Write the necessary precautions to minimize the error in the result.
R [O.D. I, II, III 2015]
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Solution:
Ans. The circuit diagram of the metre bridge is as shown below :
Working Principle : The working principle of the meter bridge is the same as that of a wheatstone bridge. The Wheatstone bridge gets balanced when :
$$ \frac{R_{2}}{R_{1}}=\frac{R_{4}}{R_{3}} $$
For the meter bridge, circuit shown above, this relation takes the form
$$ \frac{R}{S}=\frac{l_{1}}{\left(100-l_{1}\right)} $$
Determination of unknown Resistance $(R)$ : In the circuit diagram shown above, $\mathrm{S}$ is taken as a known standard resistance.
We find the value of the balancing length $l_{1}$, corresponding to a given value of $S$. We then use the relation :
$$ \frac{R}{S}=\frac{l_{1}}{\left(100-l_{1}\right)} $$
Calculation of $R$ :
By choosing (at least three) different value of $S$, we calculate $R$ each time. The average of these values of $R$ gives the value of the unknown resistance. $1 / 2$ Precautions :
(i) Make all contacts in a neat, clean and tight manner .
(ii) Select those values of $S$ for which the balancing length is close to the middle point of the wire.
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