KVPY Sample Paper KVPY Stream-SX Model Paper-8

Two wires are of same length and same area of cross-section. If first wire has resistivity \[{{\rho }_{1}}\]and Temperature coefficient of resistance \[{{\alpha }_{1}}\] but second wire has resistivity \[{{\rho }_{2}}\] and temperature coefficient of resistance\[{{\alpha }_{2}}\]. Their series Equivalent resistance is independent of small temperature changes. Then

A) \[{{\alpha }_{1}}+{{\alpha }_{2}}=0\]

B) \[{{\rho }_{1}}{{\alpha }_{1}}={{\rho }_{2}}{{\alpha }_{2}}\]

C) \[{{\rho }_{1}}{{\alpha }_{1}}+{{\rho }_{2}}{{\alpha }_{2}}=0\]

D) \[{{\rho }_{1}}{{\alpha }_{2}}+{{\rho }_{2}}{{\alpha }_{1}}=0\]

Correct Answer: C

Solution :

\[R={{R}_{1}}+{{R}_{2}}\]\[=\frac{1}{A}\left[ {{\rho }_{1}}\left( 1+{{\alpha }_{1}}t \right)+{{\rho }_{2}}\left( 1+{{\alpha }_{2}}t \right) \right]\]

For, \[\frac{dR}{dt}=0\]

Or \[{{\rho }_{1}}{{\alpha }_{1}}+{{\rho }_{2}}{{\alpha }_{2}}=0\]