Q. A uniform wire is resistance 4Ω is bent into the form of a circle of radius r. A specimen of the same wire is connected along the diameter of the circle. What is the equivalent resistance across the ends of this wire?
(a) $\displaystyle \frac{4}{(4 + \pi)} $
(b) $ \displaystyle \frac{3}{(3 + \pi)} $
(c) $ \displaystyle \frac{2}{(2 + \pi)} $
(d) $\displaystyle \frac{1}{(1 + \pi)} $
Click to See Answer :
Ans: (a)
Sol: Resistance per unit length = 4/2πr
Resistance of diameter is
Resistance of diameter is
$\displaystyle = \frac{4}{2\pi r}\times 2r = \frac{4}{\pi}$
Now, Resistance of half circle = 2 ohm
Hence , circuit has three resistances.
The resistances 2 ohm , 2 ohm & 4/π are in parallel .
$ \displaystyle \frac{1}{R}= \frac{1}{2}+\frac{1}{2} + \frac{\pi}{4}$