(C) The resistance $R$ 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

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wire of cross-sectional area $2A$

(C) The resistance $R$ 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-sectional area.For the three wires,the resistances are:$R_1 = \rho \frac{l}{A}$$R_2 = \rho \frac{2l}{A/2} = 4 \rho \frac{l}{A} = 4R_1$$R_3 = \rho \frac{l/2}{2A} = \frac{1}{4} \rho \frac{l}{A} = 0.25R_1$Comparing the resistances,$R_3 Therefore,the resistance is minimum for the wire with length $l/2$ and cross-sectional area $2A$.

Class 12 Physics Current Electricity Resistance of wire, Resistivity and Conductivity

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Three copper wires of lengths and cross-sectional areas are $(l, A)$,$(2l, A/2)$,and $(l/2, 2A)$. Resistance is minimum in

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wire of cross-sectional area $A/2$
B
wire of cross-sectional area $A$
C
wire of cross-sectional area $2A$
D
same in all the three cases

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