The $e.m.f.$ of a standard cell balances across $150\, cm$ length of a wire of potentiometer. When a resistance of $2\,\Omega $ is connected as a shunt with the cell, the balance point is obtained at $100\,cm$. The internal resistance of the cell is .............. $\Omega $
A$0.1$
B$1$
C$2$
D$0.5$
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B$1$
b (b) Using $r = R\,\left( {\frac{{{l_1}}}{{{l_2}}} - 1} \right)$ $ = 2\,\left( {\frac{{150}}{{100}} - 1} \right) = 1\,\Omega $
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In a meter bridge experiment the balance point in obtained if the gaps are closed by $2\,\Omega$ and $3\,\Omega$. A shunt of $x\,\Omega$ is added to $3\,\Omega$ resistor to shift the balancing point by $22.5\,cm$. The value of $X$ is $................$
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