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?

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

(a) Parallel

(b) 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 1

Conductor of resistance:

• 1st part: The resistivity is defined as an intrinsic property of a conductor. So with cutting the parts of a conductor, the resistivity of the substances will not change.  
• 2nd part: The new resistance of full conductor = R= pL/A
• So the new resistance is R/4 assuming the resistance of the wire was R, as length has become one fourth of the actual wire.  
• So, when connected in series, the resistance of the wire = R because the resistance when being connected in series is the summation of each resistance which comes as four times R/4.
• When connected in parallel 1/r= 1/(R/4) *4 = R/16.
• 3rd part:
• Power = V2/R. So, They are in inverse relationship.  
• So, in parallel combination, the power consumed is more.  

To learn more about conductor of resistance:

Difference between conductor, resistor and resistance

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