Question

Please solve q 12?

Answer 1

The answer is option `(B)`

Explanation:

The heat produced is

`W=Uit=Ri^2t=U^2/Rt`

But, the resistance is

`R=rho (l/s)`

The heat is doubled :

`W_1=2W=2U^2/Rt=U^2/(R/2)*t`

when the resistance is halved.

`R_1=R/2=1/2rho (l/(pir^2))=rho(l/(2pir^2))`

-Both the length and the radius are halved

`l/2` and `r/2`

`R_(l/2, r/2)=rho((l/2)/(pi(r/2)^2))=rho(l/2*(1/(pir^2/4)))=2rho(l/(pir^2))=2R`

-Both the length and the radius are doubled

`2l` and `2r`

`R_(2l,2r)=rho((2l)/(pi(2r)^2))=rho(2l*(1/(4pir^2)))=1/2rho(l/(pir^2))=R/2=R_1`

When the length is doubled

`R_(2l)=rho(2l)/s=(2rhol)/(pir^2)=2R`

When the radius is doubled

`R_(2r)=(rhol)/(pi(2r)^2)=1/4R`

The answer is option `B`, both the length and the radius are doubled.