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  4. In a meter bridge two gaps in the metallic strip are connected by 3 Ω and 9 Ω resistors. What should be the value of shunt that needs to be added to 9 Ω resistor to shift balancing point by 25 cm ?

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Q. In a meter bridge two gaps in the metallic strip are connected by $3 \,\Omega$ and $9\, \Omega$ resistors. What should be the value of shunt that needs to be added to $9\, \Omega$ resistor to shift balancing point by $25\, cm$ ?

TS EAMCET 2020

Solution:

(c) The given situation is shown below, Suppose bridge is balanced at a distance / from one end.
image
Initially in balance condition,
$\frac{3}{l}=\frac{9}{100-l}$
$ \Rightarrow l=25 \,cm$
When a shunt $S' \Omega$ is connected to $9 \Omega$ resistor balance point shifts by $25 \,cm .$
So, new balance length $=25+25=50 \,cm$
image
As meter bridge is balanced at centre point. This means resistances of left and right gap are equal.
$\Rightarrow 3=\frac{9 S}{9+S}$
$ \Rightarrow S=4.5\, \Omega$