Question

A potential difference V is applied to a conductor of length L, diameter D. How are electric field E, the drift velocity `v_(d)` and the resistance R affected when (i) V is doubled (ii)L is doubled (iii) D is doubled ?

Answer 1

We know, Electic field, `E = V/L`,
Drift velocity, `v_(d) = (eE)/(m) tau = (eV)/(mL) tau`
Resistance, `R = rho L/A = (4 rho L)/(pi D^(2))`
(i) When V is doubled, E becomes double, `v_(d)` becomes double R remains unchanged.
(ii) When L is doubled, E becomes half `v_(d)` becomes half and R becomes double.
(iii) When D is doubled, E remains unchanged, `v_(d)` is also unchanged and R becomes one-fourth.