Question 70: Current Electricity

Question

The resistance of a wire is R ohm. If it is melted and stretched to n times its original length, its new resistance will be

Accepted Answer

Volume of material remain same after stretching. As volume remains same,
$${A_1}{l_1} = {A_2}{l_2}$$
Here, $${l_2} = n{l_1}$$
$$ \Rightarrow {A_2} = {{{A_1}{l_1}} \over {{l_2}}} = {{{A_1}} \over n}$$
Resistance of wire after stretching,
$${R_2} = {{\rho {l_2}} \over {{A_2}}} = \rho {{n{l_1}} \over {{A_1}/n}} = {n^2}\rho {{{l_1}} \over {{R_1}}} = {n^2}R$$ ($$\because$$ $$R = \rho {{{l_1}} \over {{A_1}}}$$)

Answer

$$nR$$

Answer

$${R \over n}$$

Answer

$${n^2}R$$

Answer

$${R \over {{n^2}}}$$

Current Electricity

The resistance of a wire is R ohm. If it is melted and stretched to n times its original length, its new resistance will be

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