Conductor is cut into four equal parts. What will be the new resistivity

Electricity (C10)

(i) Consider a conductor of resistance ‘R’, length ‘L’, thickness ‘d’ and resistivity ‘ρ’. Now this conductor is cut into four equal parts. What will be the new resistivity of each of these parts? Why?

(ii) Find the resistance if all of these parts are connected in:

  1. Parallel
  2. Series

(iii) Out of the combinations of resistors mentioned above in the previous part, for a given voltage which combination will consume more power and why?

Answer

(i) Resistivity will not change as it depends on the nature of the material of the conductor.

(ii) The length of each part becomes L/4. ρ, A constant.

R = ρL/A

Resistance of each part = Rpart = (ρL/4)/A = R/4

(a) In parallel, Reqv = R/16 Ω

(b) In series, Reqv = R Ω

(iii) P = V2/R

If Reqv is less, power consumed will be more.

In the given case, Reqv is lesser in the parallel and power consumed will be more.