Question

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

• A. $60\pm 0.15\Omega$
• B. $135\pm 0.56\Omega$
• C. $60\pm 0.25\Omega$
• D. $135\pm 0.23\Omega$

Answer 1

Answer: (C)

The unknown resistance is given by, $R=\left(\frac{x}{100-x}\right)90$
Putting $x=40.0cm$ , $R=60\Omega$
For error analysis, $R=\left(\frac{40.0\pm 0.1}{100.0-\left(40.0\pm 0.1\right)}\right)\times 90=\left(\frac{40.0\pm 0.1}{60.0\pm 0.1}\right)\times 90$
In multiplication and division, fractional errors get added up.
Therefore, $\frac{\Delta R}{R}=\frac{0.1}{40}+\frac{0.1}{60}$
$\Rightarrow \Delta R=\frac{100}{\left(40\right)\left(60\right)}\times 0.1\times 60$ $=0.25\Omega$
Hence, $R=\left(60\pm 0.25\right)\Omega$