Question

# A uniform wire of resistance  20$$\Omega$$ having resistance  1$$\Omega / m$$  is bent in the form of circle as shown in fig. If the equivalent resistance between M and N is  1.8 $$\Omega$$ , then the length of the shorter section is :

A
2 m
B
5 m
C
1.8 m
D
18 m

Solution

## The correct option is A 2 m$$R = 20 \Omega$$$$L = 20 m$$Let the length of the shorter section be xlength of longer section is (20-x)$$R_{eq} = \frac{x(20-x)}{20} = 1.8$$   $$20x-x^{2} = 36$$   $$x^{2} - 20x + 36 = 0$$   $$(x-2)(x-18) = 0$$   $$x= 2m$$length of shorter side$$= 2m$$Physics

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