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 $(20.0 \pm 0.1) c m$

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

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.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

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