Question
The resistances in the two arms of the meter bridge are $$5\Omega $$ and $$R\Omega ,$$ respectively. When the resistance $$R$$ is shunted with an equal resistance, the new balance point is at $$1.6\,{l_1}.$$ The resistance $$'R'$$ is:
The resistances in the two arms of the meter bridge are $$5\Omega $$ and $$R\Omega ,$$ respectively. When the resistance $$R$$ is shunted with an equal resistance, the new balance point is at $$1.6\,{l_1}.$$ The resistance $$'R'$$ is:
A.
$$10\Omega $$
B.
$$15\Omega $$
C.
$$20\Omega $$
D.
$$25\Omega $$
Answer :
$$15\Omega $$
Solution :
This is a balanced wheatstone bridge condition,
$$\eqalign{ & \frac{5}{R} = \frac{{{\ell _1}}}{{100 - {\ell _1}}}\,{\text{and}}\,\frac{5}{{\frac{R}{2}}} = \frac{{1.6{\ell _1}}}{{100 - 1.6{\ell _1}}} \cr & \Rightarrow R = 15\,\Omega \cr} $$
This is a balanced wheatstone bridge condition,
$$\eqalign{ & \frac{5}{R} = \frac{{{\ell _1}}}{{100 - {\ell _1}}}\,{\text{and}}\,\frac{5}{{\frac{R}{2}}} = \frac{{1.6{\ell _1}}}{{100 - 1.6{\ell _1}}} \cr & \Rightarrow R = 15\,\Omega \cr} $$
