Question

A wire of copper having length l and area of cross section A is taken and a current I is flown through it. The power dissipated in the wire is P. If we take an aluminium wire having same dimensions and pass the same current through it, the power dissipated will be

Answer 1

Answer: The power dissipated will be increased.

Explanation:

In the given problem, A wire of copper having length l and area of cross section A is taken and a current I is flown through it. The power dissipated in the wire is P.

If we take an aluminium wire having same dimensions and pass the same current through it.

The conductivity of the copper is more than aluminium. The resistivity of the aluminium is more than the copper.

Therefore, in the case of the aluminium, the dissipation of the power will be increased as compared to the copper.

Answer 2

"After melting, the length of the wire would become double and area of cross- section will be halved.

i.e. length of wire  $l^\prime \quad =\quad 2l$

area of cross section A' = A/2

$A^\prime \quad =\quad \frac { A }{ 2 }$

$R\quad =\quad \rho \frac { l }{ A }$

$R^\prime \quad =\quad \rho \frac { l^\prime  }{ A^\prime  }$

$\Longrightarrow \quad R^\prime \quad =\quad \rho \frac { 2l }{ \frac { A }{ 2 }  } \quad =\quad 4\left( \rho \frac { l }{ A }  \right)$

$\Longrightarrow \quad R^\prime \quad =\quad 4R$

Therefore, the new resistance of the wire is 4 R.

As resistivity of material is characteristic of the given material, so it remains unchanged"