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Error and Uncertainty

R1, R2, R3 ar...

Question

$R_{1}, R_{2}, R_{3}$ are different values of R. $A, B, C$ are the null points obtained corresponding to $R_{1}, R_{2}$ and $R_{3}$ respectively. For which resistor, the value of X will be the most accurate and why?

R_{1}

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R_{2}

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R_{3}

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All same

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Solution

The correct option is B $R_{2}$
The accuracy is maximum when null point is near the mid-point and point B is nearest to the mid-point. Hence $R_{2}$ must be chosen to calculate X.

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Similar questions

△ A B C

a < b < c

r

r_{1}, r_{2}, r_{3}

A, B, C

r < r_{1} < r_{2} < r_{3}

△ A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = \frac{r_{1} r_{2} r_{3}}{r}

a (r r_{1} + r_{2} r_{3}) = b (r r_{2} + r_{3} r_{1}) = c (r r_{3} + r_{1} r_{2})

r

r_{1}, r_{2}, r_{3}

A B C

a, b, c

R_{1}, R_{2}

R_{3}

r_{1}, r_{2}, r_{3}

A B C

r

r_{1} r_{2} r_{3} - r (r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1})

Δ

r_{1} + r_{2} + r_{3} - r = 4 R

r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = Δ^{2}

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