Find the equivalent resistance between A and B
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A potential difference V is applied between A and B.
Let a total current of x+y flows through the circuit. The current distribution is as shown. Equivalent resistance of the circuit is thus given by,
Req = V/ x+y _[i]
In loop AEFBA, -yR - yR - (y+z) R+V = 0
or, V = (3y + z) R _[ii]
In loop ACFEA, - xR - zR + yR + yR = 0
=> x + z = 2y _[iii]
In loop ACDBFEA,
-xR - ( x -z)R - (x-z)R + (y+z)R + 2yR = 0
=> z = x - y _[iv]
From [iii] and [iv]
z = y/2 _[v]
From [i] and [ii] we have
Req = [ 3y+z/ x+y] R
From [v], y = 2z, from [iii], x = 3z
=> Req = [ 3(2z)+ z/ 3z + 2z ] R
= 7R/5
∴ The Equivalent Resistance between A and B is 7R/5
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