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The entire network shown here, has unifo...

The entire network shown here, has uniform wire having resistance per unit length `1Omega//m`. It is place in a uniform but time varying magnetic field (directed into the plane). If magnetic field increasing at a rate of IT/s, the ratio `I_(1)//I_(2)` equals

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The correct Answer is:
`(1)/(22)A (from F to E)`
Loop `ABCD`: Area `= 1 xx 1 = 1 m^(2)` ltbr. Flux: `phi_(1) = B(Area) = B xx 1 = B`
Induced emf: `e_(1) = (dphi_(1))/(dt) = (dB)/(dt) = 1 V`

Loop `EBCF`: Area `= 1 xx ((1)/(2)) = (1)/(2)m^(2)`
Flux: `phi_(2) = B(Area) = (B)/(2)`
Induced emf: `e_(2) = (dphi)/(dt) = (1)/(2)(dB)/(dt) = (1)/(2) V`
Both emfs are anticlockwise sence as shown in figure.
Apply Kirchhoff's law:
`e_(1) = 1I + 1I + 1I - 1(I_(1) - I)` `rarr` `1 = 3I - I_(1) + I`
`rarr` `4I - I_(1) = 1` (i)
`e_(2) = 1(I_(1) - I) + (1)/(2)I_(1) + 1I + (1)/(2)I_(1)`
`rarr` `6I - 2I_(1) = 1` (ii)
Solve (i) and (ii) to get
`I = (7)/(22)A, I_(1) = (6)/(22)A`
So current in `EF`: `I_(1) - I = (6)/(22) - (7)/(22)A` (from `Eto F`)
`= (1)/(22)A` (from `F to E`)
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