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Question
A resistance R is to be measured using a meter bridge. Student chooses the standard resistance S to be 100Ω. He finds the null point at l1 = 2.9 cm. He is told to attempt to improve the accuracy. Which of the following is a useful way?
Options
He should measure l1 more accurately.
He should change S to 1000Ω and repeat the experiment.
He should change S to 3Ω and repeat the experiment.
He should give up hope of a more accurate measurement with a meter bridge.
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Solution
He should change S to 3Ω and repeat the experiment.
Explanation:
⇒ `R = S(l_1/(100 - l_1)) = 100 2.9/97.1` = 2.98Ω
In this problem, the balanced Wheatstone bridge is to be used.
Condition of balanced wheatstone bridge: The bridge is said to be balanced if the ratio of the resistances in the same branch is equal `R/S = (l_1/(100 - l_1))`
Wheatstone bridge is an arrangement of four resistances which can be used to measure one unknown resistance of them in terms of rest.
The percentage error in R can be minimised by adjusting the balance point near the middle of the bridge, i.e., when l, is close to 50 cm. This requires a suitable choice of S.
Since, `R/S = (l_1/(100 - l_1))`
Since here, R : S = 2.9 : 97.1 then the value of S is nearly 33 times that of R. In order to make this ratio 1:1, it is necessary to reduce the value of S almost 1/33 times, i.e., nearly 3Ω.
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Write balancing condition of a Wheatstone bridge.
