Question

two manganin wire whose length are in the ratio of 1:2 and whose resistance are in ratio of 1:2 connected in series find what will be the ratio of the drift velocity of free electrons in two wires

Answer 1

Dear Student,
Here in this question the ratio of the length of two manganin wire is 1:2 and resistance of two manganin wire is 1:2 .
Now we know that , R$=\rho \frac{l}{A}$
So ,
$$\begin{gathered} \frac{R_1}{R_2}=\frac{l_1}{l_2}\frac{A_2}{A_1} \\ \Rightarrow \frac{1}{2}=\frac{1}{2}\frac{A_2}{A_1} \\ \Rightarrow A_1=A_2 \end{gathered}$$
Again we know that the drift velocity is , $v_d=\frac{I}{neA}$
Therefore , $$\begin{gathered} v_d\propto \frac{1}{A}and \\ \frac{v_{d_1}}{v_{d_2}}=\frac{A_2}{A_1}=1\left[\because A_1=A_2\right] \\ \Rightarrow v_{d_1}=v_{d_2} \end{gathered}$$
Regards