Question

During an experiment with a meter bridge, the galvanometer shows a null point when the jockey is pressed at 40.0 cm using a standard resistance of $90\Omega$. The least count of the scale used in the meter bridge is 1mm. The unknown resistance is

• A. \((60 \pm 0.15) \Omega\)
• B. \((135 \pm 0.05) \Omega\)
• C. \((60 \pm 0.25) \Omega\)
• D. \((135 \pm 0.23) \Omega\)

Answer 1

The correct option is C \((60 \pm 0.25) \Omega\)

We have,
$X=\frac{S{l}_1}{l_2}$
where
$l_1=40\pm 0.1cm=40\pm 0.25\%$
$l_1=60\pm 0.1cm=60\pm 0.16\%$
$\frac{\Delta x}{x}=\frac{\Delta l_1}{l_1}+\frac{\Delta l_2}{l_2}$
$=0.25+0.16$
$=0.41\%$
$X_m=\frac{90\times 40}{60}$
$60cm$
$\therefore =X=60\pm 0.41\%$
$=60\pm 0.25)\Omega$