A uniform wire of resistance 4 ohm is bent into the form of a circle of radius

Discussion Forum : Current Electricity

Question -

A uniform wire of resistance 4 ohm 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?

Options:

A .

\frac{4}{4 + π}

ohm

B .

\frac{3}{3 + π}

ohm

C .

\frac{2}{2 + π}

ohm

D .

\frac{1}{1 + π}

ohm

Answer: Option A
:
A

Circumference of the circle = $2 π r$
Therefore the resistance per unit length of the wire = $\frac{R}{2 π r}$
where r= 4 ohm is the resistance of wire
Now the length of the specimen connected along the diameter = 2r
Therefore the resistance of this specimen is
$R_{1} = \frac{R}{2 π r} \times 2 r = \frac{R}{π}$
also the resistance of each semicircle is
$R_{2} = \frac{R}{2}$
equivalent resistance R' across the specimen is given by
$\frac{1}{R^{'}} = \frac{2}{R} + \frac{2}{R} + \frac{π}{R} = \frac{4 + π}{R}$
$R^{'} = \frac{R}{4 + π} = \frac{4}{4 + π}$ ohm

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Discussion Forum : Current Electricity

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