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infinite square brackets have been made by infinite wires .between each junction ,the resistance is r .find equivalent resistance between points A AND B
24R=resitance of whole grid,R"=resistance of AB
I=total current of grid
I"=current through AB
ALSo Voltage V is applied
=>V=IR=I".R" --------------(1)
we find by using symmetry princiiple and superpositon of current from four wires taht I/2 current flows through part AB
Also from (1)...
IR=I"R"
=> IR=I/2 R"
=>R"=2R
62seems that eureka has made a small mistake in taking the current..
seems that eureka has not explained it completely :) :P
1We assume dat der's a battery of emf V connected b/w pt.s P and Q .
If current supplied is I, then here superposition principle says :
if current coming to P i.e. I / 4 and spreading in the circuit and the current pasing away through Q i.e. I / 4 are superimposed , then resultant current is half the current supplid by the battery.
so, V = I Req
and , from circuit equation , V = ( I / 2) . r
so , I . Req = ( I / 2) . r
so , Req = r / 2.
