Question

A uniform wire of resistance 4R is bent in the form of circle the effective resistance between the ends of any diameter of the circle is
a) 2R b) R c) R/2 d) 4R

Answer 1

Answer:

a) 2R

Explanation:

Reff=1/(1/4R)*(1/4R)

=1/(1/2R)

=2R

Answer 2

a) 2R

Explanation:

Given:

resistance of the wire is $4R$

When this wire is bent into circle and the resistance is taken between any two diametrically opposite points then the length of the wire is halved and the two halves are in parallel to each other.

We have the relation between the length of wire and the resistance as:

$R=\rho.\frac{l}{a}$

where:

$\rho=$ resistiviy of the wire material

$l=$ length of the wire

$a=$ cross sectional area of the wire

Now initially:

$4R=\rho.\frac{l}{a}$

Resistance of the wire when the length is halved:

$R'=\rho.\frac{\frac{l}{2}}{a}$

$R'=\frac{1}{2}\times\rho\frac{l}{a}$

$R'=\frac{1}{2}\times 4R$

$R'=2R$

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TOPIC: resistivity

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