The electric resistance of a certain wire of iron is R. If its length and radius are both doubled, then

detailed solution

Correct option is B

The formula for resistance of wire isR=ρlAwhere ρ = specific resistance of the wire⇒R∝lA⇒R∝1r2           ∵     A=πr2∴    R1R2=  l1l2 ×  r22r12                                                               ....iGiven,   l1 =l,  l2 =2l,  r1=r,  r2=2r,  R1=RSubstituting these values in Eq. (i), we haveR1R2=  l2l ×  2r2r 2R1R2=2  and   R2 =R2Therefore, resistance will be halved.Now the specific resistance of the wire does not depend on the geometry of the wire, hence, it remains unchanged.Aliter: R ∝ lr2  ⇒   R1R2 =   l2 l1  ×   r12r22 =  21  ×  212=12⇒   R2  =  R12,  specific resistance doesn't depend upon length and radius.