A) \[\frac{3}{\sqrt{\rho }}\]
B) \[\frac{\sqrt{3}}{\rho }\]
C) \[\frac{5}{\sqrt{\rho }}\]
D) \[\frac{\sqrt{5}}{\rho }\]
Correct Answer: A
Solution :
\[\text{Volume =Area }\!\!\times\!\!\text{ length}\] \[3=Al\] \[A=\frac{3}{l}\] Resistance \[R=\rho \frac{l}{A}\] \[3=\frac{\rho l}{\left( \frac{3}{l} \right)}=\frac{\rho {{l}^{2}}}{3}\] \[{{l}^{2}}=\frac{9}{\rho }\] \[\Rightarrow \] \[l=\frac{3}{\sqrt{\rho }}\]
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