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BITSAT 2022 Paper

Section: Physics

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Question : 27 of 130

Marks: +1, -0

In the arrangement shown in figure, when the switch

S_2

is open, the galvanometer, shows no deflection for

l=50\,\mathrm{cm}

when the switch

S_2

is closed, the galvanometer shows no deflection for

l=0.416\,\mathrm{m}

. The internal resistance

(r)

6\,\mathrm{V}

$2\,\Omega$
$3\,\Omega$
$5\,\Omega$
$9\,\Omega$

Solution: 👈: Video Solution

When

S_2

open.

Assume resistance of

X\gamma =R

Resistance of wire per unit length,

x=\frac{R}{L}=R\,\Omega\,\mathrm{m}^{-1}

\because I=\frac{E_0}{R}

Now, the potential drop across 50 cm length is

6\,\mathrm{V}

, so

\frac{E_0}{R}\times R\times \frac{50}{100}=6

\Rightarrow E_0=12\,\mathrm{V}

When

S_2

closed, potential drop across

0.416\,\mathrm{cm}

length,

V_1=\frac{E_0}{R}\times R\times 0.416=12\times 12\times 0.416\approx 5\,\mathrm{V}

Hence,

E - I r = 5\,\mathrm{V}

\Rightarrow 6 - I r = 5

\because I = \frac{5}{10}

\therefore 6-5 = \frac{5}{10} r

\Rightarrow r = 2\,\Omega

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