(a) A Nichrome wire of length L and radius r | vedclass

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(N/A) $(i)$ The resistance $R$ of a wire is directly proportional to its length $L$ $(R \propto L)$. When the length is doubled,the resistance also be

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(N/A) $(i)$ The resistance $R$ of a wire is directly proportional to its length $L$ $(R \propto L)$. When the length is doubled,the resistance also becomes double. Therefore,the new resistance is $2 	imes 10 \, \Omega = 20 \, \Omega$.$(ii)$ The resistance $R$ is inversely proportional to the square of the diameter $D$ $(R \propto 1/D^2)$. When the diameter is doubled,the resistance becomes $1/4$ of its original value. Therefore,the new resistance is $10/4 \, \Omega = 2.5 \, \Omega$.$(b)$ The heating elements of electrical devices are made of alloys because alloys have a much higher resistivity than their constituent metals. Furthermore,alloys do not oxidize (burn) readily even at high temperatures,which increases the durability and efficiency of the heating element.

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