A wire of length ' $l$ ' is gradually stretched so that its length increases to 3 I. If its original

Question

A wire of length ' $l$ ' is gradually stretched so that its length increases to 3 I. If its original resistance is $R$, then its new resistance will be\

Professor PC Thomas Classes · Answer

(c):Since the volume of the wire remains constant, $A l=A^{\prime}$\ where $A^{\prime}$ and $I^{\prime}$ are the cross-section and length of wire after stretching.\ $A I=A^{\prime}(3 I)$\ $A^{\prime}=\frac{A}{3}$\ New resistance, $R^{\prime}=\frac{ho l^{\prime}}{A^{\prime}}=\frac{ho(3 l)(3)}{A}=9\left(\frac{ho l}{A}ight)$\ $R^{\prime}=9 R$\