Question

Consider a Conductor of resistance 'R', length 'L' ,thickness 'd' and resistivity 'ρ'.
Now this conductor is cut into 4 equal parts. Find the resistance if all the parts are connected in:
i) Parallel
ii) Series

Answer 1

Answer:

i) Resistivity will remain same.

ii) a)

b)

iii)Parallel connection consume more power because it have low equivalent resistance.

Explanation:

Given that

Resistance =R

Length =L

Thickness=d

Resistivity =ρ

Now when wire cuts in 4 equal parts

L'= L/4

i)

We know that resistivity is a material properties and does not depends on the physical dimensions.So even wire cuts in 4 equal but still resistivity will remain same.

So the answer is, resistivity will be same.

ii)

We know that

R = ρ L/A

When L become 1/4 th then resistance for each part is R'

R' =  ρ L'/A  

L'= L/4

R' =  ρ L/4A  

R'= R/4

It means that resistance will become one forth of initial resistance

a)Parallel connection:

We know that equivalent resistance given as

b)Series connection :

iii)

We know that Power P given as

P=V.I =V²/R                      ( V= IR)

For given voltage parallel connection consume more power because it have low equivalent resistance.