Figure shows an experimental setup to find the value of an unknown resistance $R_{x}$ using a meter bridge. AB is uniform meter bridge wire of length L =100 cm (exactly). When sliding jockey is at J (AJ = X), the galvanometer shows zero deflection. Length AJ is measured by a meter scale having least count of 1mm. In experiment known resistance is taken as $20 Ω$ (exactly) and length AJ was found to be $(20.0 \pm 0.1) c m$

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Value of $R_{x} = (5.00 \pm 0.02) Ω$

Value of $R_{x} = (5.00 \pm 0.03) Ω$

To minimize fractional error the known resistance should be very close to
$R_{x}$

When $x = \frac{L}{2},$ fractional error is minimized

answer is A, C, D.

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Detailed Solution

$\frac{R_{x}}{x} = \frac{R}{1 - x} \frac{R_{x}}{20} = \frac{20}{80} R_{x} = 5 R_{x} = \frac{x}{1 - x} [R] Δ R_{x} = R [\frac{Δ x (1 - x) - x (- Δ x)}{{(1 - x)}^{2}}] Δ R_{x} = 0.03 Ω e r r o r w i l l b e m i n i m i z e d w h e n n u l l - p o i n t i s f o u n d a t m i d d l e o f w i r e .$