Q. 29 3.9( 34 Votes )

(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:

(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 :

(i) Let the initial resistance be R


Length be L


Thickness be d and


Resistivity be ρ


Now resistivity is given by



When the resistance is cut into 4 equal pieces, then the cross sectional area remains same before and after.


Hence resistivity becomes-



Hence, resistivity remains same.


(ii)When all parts are connected in series, then equivalent resistance,



Now the length of each part becomes, L/4 and resistivity and Area of cross section remains same, then-



(iii)When all resistors are connected in parallel-




(iii)Power loss in a resistor in form of heat is given by is given by



Where,


i = is the current flowing through it.


Hence, power loss is in direction proportion to resistance which means more resistance, more power loss.


Hence, resistors in series will consume more power than parallel.


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