If a wire of resistance R is melted and recas | vedclass

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(A) The resistance of a wire is given by the formula $R = \rho \frac{L}{A}$,where $\rho$ is the resistivity,$L$ is the length,and $A$ is the cross-sec

Vedclass · Accepted Answer

$R / 4$

Vedclass · Answer

(A) The resistance of a wire is given by the formula $R = ho \frac{L}{A}$,where $ho$ is the resistivity,$L$ is the length,and $A$ is the cross-sectional area.When the wire is melted and recast to half its length $(L' = L / 2)$,its volume remains constant.Since $V = A 	imes L$,we have $A 	imes L = A' 	imes L'$.Substituting $L' = L / 2$,we get $A 	imes L = A' 	imes (L / 2)$,which implies $A' = 2A$.The new resistance $R'$ is given by $R' = ho \frac{L'}{A'}$.Substituting the new values: $R' = ho \frac{L / 2}{2A} = \frac{1}{4} 	imes ho \frac{L}{A}$.Therefore,$R' = R / 4$.

If a wire of resistance $R$ is melted and recast to half of its length,then the new resistance of the wire will be

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