A) It is the same in all three cases
B) Wire of cross-sectional area 2 A
C) Wire of cross-sectional area A
D) Wire of cross-sectional area \[\frac{1}{2}A\]
Correct Answer: B
Solution :
Key Idea: The resistance for a wire is proportional to ratio of length and cross-sectional area of wire. The relation between length and area is \[R=\frac{\rho L}{A}\] ........(i) \[\rho \] being specific resistance is the proportionality constant and depends on nature of material. First case is not possible as we cannot approach the true value Length \[\frac{L}{2}\], area = 2A Putting in Eq, (i) \[{{R}_{3}}=\frac{\rho (L/2)}{2A}=\frac{\rho L}{4A}\] Length = L, area = A putting in Eq. (i), we have \[{{R}_{1}}=\frac{\rho L}{A}\] Length = 2L, area \[=\frac{A}{2}\] Putting in Eq. (i), we have \[{{R}_{2}}=\rho \frac{2L}{A/2}\frac{4\rho L}{A}\] As it is understood from above, that \[{{R}_{3}}\] is minimum. Thus, option is correct.
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