Question

A conductor of length / is connected to a $DC$ source of potential $V$. If the length of the conductor is tripled by gradually stretching it, keeping $V$constant, how will
(i) drift speed of electrons and
(ii) resistance of the conductor be affected? Justify your answer.

Answer 1

i)

drift speed of an electron

$v_d\propto \frac{1}{l}$

when the wire length is tripled, drift velocity gets one third

ii)

resistance of conductor

$R=\rho \frac{l}{a}$

mass of the wire remains the same in both the conditions

mass before stretching = mass after strecting

$m_1=m_2$

$v_1{\rho }_1=v_2{\rho }_2$

$a_1{l}_1=a_2{l}_2$

$a_{1}l=a_2\left(3l\right)\Rightarrow a_2=\frac{a_1}{3}$

$R^{\prime }=\rho \frac{l^{\prime }}{a^{\prime }}=\rho \frac{3l}{\frac{a}{3}}=9\frac{\rho l}{a}=9R$

new resistance is 9 times the original resistance.