A wire of resistance $12 \mathrm{ohms}$ per metre is bent to form a complete circle of radius $10…
A wire of resistance $12 \mathrm{ohms}$ per metre is bent to form a complete circle of radius $10 \mathrm{~cm}$. The resistance between its two diametrically opposite points, A and B as shown in the figure, is :
$6 \Omega$
$0.6 \pi \Omega$
$3 \Omega$
$6 \pi \Omega$
Solution
Total resistance of wire $=12 \Omega \times 2 \pi \times 10^{-1}$
$=2.4 \pi$
Resistance of each half $=\frac{2.4 \pi}{2}=1.2 \pi$
and as about diameter both parts are in parallel
$\text {Req. }=\frac{1.2 \pi}{2}=0.6 \pi \Omega$
