Physics · Kirchhoff's laws and their applications, Wheatstone bridge, Metre Bridge
During an experiment with a metre bridge, the galvanometer shows a null point wh
During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at \( 40.0 \mathrm{cm} \) using a standard resistance of \( 90 \Omega, \) as shown in the figure. The least count of the scale used in the metre bridge is 1 mm. The unknown resistance is
- A. \( 60 \pm 0.15 \Omega \)
- B. \( 135 \pm 0.56 \Omega \)
- C. \( 60 \pm 0.25 \Omega \)
- D. \( 135 \pm 0.23 \Omega \)
Step-by-step solution
Using the metre bridge formula X = S * L/(100-L), with S = 90 Ω and L = 40.0 cm gives X = 60 Ω. The error ΔX is found from ΔX = X * ΔL * (1/L + 1/(100-L)) with ΔL = 0.1 cm (least count). Substituting gives ΔX = 60 * 0.1 * (1/40 + 1/60) = 60 * 0.1 * (0.025 + 0.01667) = 0.25 Ω. Hence, X = 60 ± 0.25 Ω.
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