Current Electricity - Result Question 16
17. There are three copper wires of length and cross sectional area $(L, A),(2 L, \frac{1}{2} A),(\frac{1}{2} L, 2 A)$. In which case is the resistance minimum? [1997]
(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 $\frac{1}{2} A$
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Answer:
Correct Answer: 17. (b)
Solution:
- (b) $R=\rho \frac{l}{A}$
$R_1=\rho \frac{L}{A}$
$R_2=\rho \frac{2 L}{A} \times 2$
$R_3=\rho \frac{L}{2.2 A}=\frac{\rho L}{4 A}$
$\Rightarrow R_3<R_1<R_2$
