| Consider the meter bridge shown in figure |
 |
| The resistance X has temperature coefficient \[{{\alpha }_{1}}\]and from RB \[\left[ 9\Omega \,shown \right]\]has \[{{\alpha }_{2}}\] For shown situation balance point is at 10 cm from left end, if temperature of system increases by \[\Delta T\] due to joule heating than the shift in the balance point is [Assume that only the resistance of X and RB changes due to change in temperature and there is no other effect] |
A) \[9\left( {{\alpha }_{1}}-{{\alpha }_{2}} \right)\Delta T\]
B) \[9\left( {{\alpha }_{1}}+{{\alpha }_{2}} \right)\Delta T\]
C) \[\frac{1}{9}\left( {{\alpha }_{1}}+{{\alpha }_{2}} \right)\Delta T\]
D) \[\frac{1}{9}\left( {{\alpha }_{1}}-{{\alpha }_{2}} \right)\Delta T\]
Correct Answer: A
Solution :
| From balance condition, \[\frac{X}{Y}=\frac{1}{100-1}\] |
| For given situation, \[y=9\Omega \] and \[l=10cm\] |
| \[\frac{dX}{X}-\frac{dY}{Y}-\frac{dl}{l}+\frac{dl}{100-l}\] |
| As error sign is known or we can say these are systematic error we will substitute them with sign |
| \[{{\alpha }_{1}}\Delta T-{{\alpha }_{2}}\Delta T=dl\left[ \frac{1}{10}+\frac{1}{90} \right]\Rightarrow dl=9({{\alpha }_{1}}-{{\alpha }_{2}})\Delta T\] |
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