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

Question

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

Infinity Learn · Accepted Answer

Let the resistance of the shorter part MN be x. Total resistance is $$20$$. Hence the resistance of longer MN part will be (20$$ $$-x). With respect to M and N, the portions are connected in parallel. Hence∴ $$Req=(20$$−$$x)$$×$$x(20$$−$$x)+x=1$$⋅$$8Solving$$, we get x $$=$$ $$2mThe$$ resistance is $$1$$Ω$$/$$ m and hence the length of shorter part $$MN=$$ $$2$$ x $$1=$$ $$2m$$

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

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

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