Question

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?

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Answer 1

Answer:

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

(2)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 the 1/Reqv = 1/Reqv +1/Reqv +1/Reqv +1/Reqv = 4/Reqv = 16R →Reqv = R/16 Ω

(b) In series the Reqv= R/4+ R/4 +R/4+R/4=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.

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