Q.442. Solution of electric network.

Question 442.
What is the current passing through 5 ohm resistor in given circuit ?

Answer 442.
Refer to the figure as under.

Currents, x, y and z and their combinations are shown in different branches.
For the loop ABD,
6x - 2y + 5z = 0 ... ( 1 )
For the loop ABC,
5z + 6(y+z) - 2(x-z) = 0
=> 2x - 6y - 13z = 0 ... ( 2 )

For the loop BCD,
6(y+z) + 2y + 2(x+y) = 10
=> 2x + 10y + 6z = 10 ... ( 3 )

Solving eqns. ( 1 ), ( 2 ) and ( 3 ) using 
Wolfram Alpha Link
z = - 0.4 A
=> current through 5 ohm resistor is 0.4 A.

Link to YA!