Current Electricity Ques 2
2. A wire of resistance $12$ ohms per meter is bent to form a complete circle of radius $10 \mathrm{cm}$. The resistance between its two diametrically opposite points, $\mathrm{A}$ and $\mathrm{B}$ as shown in the figure, is
[2009]
(a) $3 $ $\Omega$
(b) $6 $ $\pi $ $\Omega$
(c) $6 $ $\Omega$
(d) $0.6 $ $\pi$ $ \Omega$
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Answer:
Correct Answer: 2.(d)
Solution: (d)
Length of wire $=2$ $ \pi $ $\mathrm{r}=2 \pi(0.1)=0.2$ $ \pi$ $ \mathrm{m}$
$ \text { Resistances of complete circle/wire }=12 \times 0.2 \pi $
$ =2.4 $ $\pi $ $\Omega $
$ \therefore \text { Resistance of each semi-circle }=1.2 $ $\pi $ $\Omega $
$ \text { Hence, equivalent resistance, } $
$ \quad \mathrm{R}_{\mathrm{AB}}=\frac{1.2 \pi}{2}=0.6 $ $\pi$ $ \Omega$
BETA
