A triangle is constructed using wires AB, BC and CA of same material and of resistance α, $$2$$α and $$3$$α, respectively. Another wire of resistance α$$/3$$ from A can make a sliding contact with wire BC. Find the maximum resistance of the network between points A and the point of sliding wire with BC.

Question

A triangle is constructed using wires AB, BC and CA of same material and of resistance α,  $$2$$α and  $$3$$α, respectively. Another wire of resistance α$$/3$$ from A can make a sliding contact with wire BC. Find the maximum resistance of the network between points A and the point of sliding wire with BC.

Infinity Learn · Accepted Answer

∴   $$1Req$$ $$=$$ $$1$$α$$+x+3$$α $$+15$$α−$$x=$$α$$5$$α−x $$+3$$ α$$+x$$ $$5$$α−x−α α$$+x$$αα$$+x$$ $$5$$α−$$x1Req=5$$α$$2$$−αx $$+15$$α$$2$$−$$3x2+12$$α$$x+a2+$$αxαα$$+x$$ $$5$$α−$$xReq=$$αα$$+x$$ $$5$$α−$$x21$$α$$2+12$$αx−$$3x2$$ ⇒   dReqdx $$=$$ $$0Reqmax=$$ $$311$$ α

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

A triangle is constructed using wires AB, BC and CA of same material and of resistance α, 2α and 3α, respectively. Another wire of resistance α/3 from A can make a sliding contact with wire BC. Find the maximum resistance of the network between points A and the point of sliding wire with BC.

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material