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In the network in given find l(1), l(2)...

In the network in given find `l_(1), l_(2)` and l.

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Applying Kirchhoff's junction rule to c or f
`l= l_(1)+l_(2)` …..(i)
Applying loop rule to abcfa
`- 3 fl_(2) - 5 + l_(1) + 4 l_(1) = 0 `

`implies 5l_(1) - 3 l_(2) = 5 ` ….(ii)
Appling loop rule to abdea
`- 3l_(2) - 2 l - l + 8 = 0 `
` 3l + 3l_(2) = 8 `
` implies 3 (l_(1) + l_(2))+ 3 l_(2) = 8 ` (Using equation (i))
`implies 3l_(1) + 6 t_(2) = 8 ` .....(iii)
Equation (ii) ` xx 2 + ` Equation (iii) we get
`10 l_(1) - 6l_(2) + 3l_(1) + 6l_(2) = 10 +8`
`implies 13l_(1) = 18 `
`implies l_(1) = (18)/( 13) A `
Putting value of `l_(1)` in equation (ii) , we get
` 5 xx ( 18)/( 13) - 3 l_(2) = 5`
`implies l_(2) = ( ( 90)/( 13) - 5)/( 2) = ( 90 -65)/( 13 xx 3 ) `
`= ( 25)/( 39) A`
`l = l_(1) + l_(2) = ( 18) /( 13) + ( 25)/( 39) = ( 54 + 25)/( 39) = ( 79)/( 39) A`
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