Current Electricity Ques 37
37. When a wire of uniform cross-section $a$, length $l$ and resistance $R$ is bent into a complete circle, resistance between any two of diametrically opposite points will be [2005]
(a) $\frac{R}{4}$
(b) $4 R$
(c) $\frac{R}{8}$
(d) $\frac{R}{2}$
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Answer:
Correct Answer: 37.(a)
Solution:
$ R _{AB}=\frac{1.2 \pi}{2}=0.6 \pi \Omega $
$R / 2$
$ R _{eq}=\frac{R_1 R_2}{R_1+R_2}=\frac{(\frac{R}{2} \cdot \frac{R}{2})}{\frac{R}{2}+\frac{R}{2}} \quad \therefore R _{eq}=\frac{R}{4} $
If a wire of resistance $R$ is bent in the form of circle, the effective resistance between the ends of diameter is $R / 2$
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