During an experiment with a metre bridge, the galvanometer shows … - Vidyadip

MCQ

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

A
$60 \pm 0.15 \ \Omega$
B
$135 \pm 0.56 \ \Omega$
✓
$60 \pm 0.25 \ \Omega$
D
$135 \pm 0.23 \ \Omega$

✓

Answer

Correct option: C.

$60 \pm 0.25 \ \Omega$

c
For balanced meter bridge

$\frac{X}{R}=\frac{\ell}{(100-\ell)}$

$\frac{X}{40}=\frac{90}{60} \Rightarrow X=60 \Omega$

$X=R \frac{\ell}{(100-\ell)}$

$\frac{\Delta X}{X}=\frac{\Delta \ell}{\ell}+\frac{\Delta \ell}{100-\ell}=\frac{0.1}{40}+\frac{0.1}{60}$

$\Delta X=0.25$

$\text { so अत: } X=(60 \pm 0.25) \Omega$

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