Question

A conductor of length l is connected across an ideal cell of emf E. Keeping the cell connected, the length of the conductor is increased to 2l by gradually stretching it. If R and R' are initial and final values of resistance and v_d and `v_d^'` are initial and final values of drift velocity, find the relation between

1. R' and R and
2. `v_d^'` and v_d.

Answer 1

A conductor of length is connected to an ideal cell of emf E. To keep the cell connected, gradually stretch the conductor to reach a length of 2l. Hence, the volume of the conductor remains constant.

i. Al = A' l'

Since l' = 2l

A' = `A/2`

R = `rho 1/A`

R' = `rho (l')/(A')`

= `rho (2l)/(A/2)`

= 4 R

ii. v_d = `(e E tau)/m`

`(v_d^')/v_d = (E')/E`

= `(V/(2l))/(V/l)`

= `l/(2 l)`

= `1/2`