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In the network in given figure find I(...

In the network in given figure find `I_(1),I_(2)` and i.

Text Solution

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Applying kirchhoff,s junction rule of c or f
`I = I_(1) + I_(2) " "…….(i)`
Applying loop rule of abcfa
` - 3l_(2) - 5 + I_(1) + 4l_(1) = 0`
` rArr 5l_(1) - 3l_(2) = 5" "………..(ii)`
Applying loop rule to abdea
` - 3l_(2) - 2l - l + 8 = 0`
`3l + 3l_(2) = 8`
`rArr 3(l_(1) + l_(2)) + 3l_(2) = 8 ` ( Using equation (i))
`rArr 3l_(1) + 6l_(2) = 8" ".......(iii)`
Equation (ii) `xx 2` + Equation (iii) , we get
`10l_(1) - 6l_(2) + 3l_(1) + 6l_(2) = 10 + 8`
`rArr 13l_(1) = 18`
` rArr l_(1) = (18)/(13)A`
Putting value of `l_(1) ` in equation (ii) , we get
` 5 xx (18)/(13) - 3l_(2) = 5`
` rArr l_(2) = ((90)/(13) - 5)/(3) = (90-65)/(13 xx 3)`
` = (25)/(39) A`
`rArr = l_(1) + l_(2) = (18)/(13) + (25)/(39) = (54 + 25)/(39) = (79)/(39) A`
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