Resistivity

volume is constant (so when length is doubled area is halved)

hw can u be sure abt it dat area is halved.... can' t it be dat radius is halved.....

sum1 plz help me out in di.s..

see the quantity of the wire remains the same..
so its Volume (V) has to remain constant..

and V = length * area of cross section

so inverse relation between length and area of cross section

hope now u got it cleared.

apply,

A₁L₁=A₂L₂ (AS VOLUME REMAINS CONSTANT)

WHERE A₁ IS INITIAL AREA OF CROSS SECTION AND L₁ IS INITIAL LENGTH OF ROD.

A₂ IS NEW AREA OF CROSS SECTION AND L₂ IS NEW LENTH OF ROD.

ACC. TO QUESTION ----

A₁L₁=A₂.2L₁

A₂A₁=12 ............................EQ.ⁿ 1

SO , NEW AREA OF CROSS-SECTION BECOMES HALF OF INITIAL AREA AND NEW RADIUS BECOMES 1√2 TIMES OF INITIAL RADIUS..

NOW,

R_INTIAL = p L₁A₁

R_NEW = p L₂A₂ (BECAUSE AS NATURE OF MATERIAL REMAINS SAME RESISTIVITY REMAINS SAME)

R_NEW= p 2L₁A₂

R_INITIAL R_NEW =12 A₂A₁

R_INITIAL R_NEW= 12.12 (FROM EQ.ⁿ 1)

R_INITIAL R_NEW=14

R_NEW=4.R_INITIAL
SO , NEW RESISTANCE BECOMES 4 TIMES OF INITIAL RESISTANCE BY DOUBLING THE LENGTH OF ROD.......

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i 've understood da concept....
par ye last post mein nihal kya saabit karna chaah raha hai