Current Electricity Charging Discharging Of Capacitors Question 169
Question: A wire of resistor R is bent into a circular ring of radius r. Equivalent resistance between two points X and Y on its circumference, when angle XOY is a, can be given by
Options:
A) $ \frac{R\alpha }{4{{\pi }^{2}}}(2\pi -\alpha ) $
B) $ \frac{R}{2\pi }(2\pi -\alpha ) $
C) R (2p ? a)
D) $ \frac{4\pi }{R\alpha }(2\pi -\alpha ) $
Show Answer
Answer:
Correct Answer: A
Solution:
Here $ R _{XWY}=\frac{R}{2\pi r}\times (r\alpha )=\frac{R\alpha }{2\pi } $
$ ( \because ,\alpha =\frac{l}{r} ) $ and $ R _{XZY}=\frac{R}{2\pi r}\times r(2\pi -\alpha )=\frac{R}{2\pi }(2\pi -\alpha ) $
$ R _{eq}=\frac{R _{XWY}R _{XZY}}{R _{XWY}+R _{XZY}}=\frac{\frac{R\alpha }{2\pi }\times \frac{R}{2\pi }(2\pi -\alpha )}{\frac{R\alpha }{2\pi }+\frac{R(2\pi -\alpha )}{2\pi }} $
$ =\frac{R\alpha }{4{{\pi }^{2}}}(2\pi -\alpha ) $
BETA
