In the given circuit, mark the correct statement// statements.

Options

A. The current through 10 V battery is `35//4A`.
B. The current through 5 V battery is `5//4A.`
C. The current through upper conducting wire is `15//8A`.
D. The current through lower conducting wire is `25//8A`.

Answer

B, C

Explanation

b.,c.

From diagram it is clear `I_3 = ((x+5)-x)/2 = 5/2A`
and `I_7 = (10-0)/2 = 5A`
At node a
`I_3 = I_1 + x/4 or 5/2 = I_1 + x/4`
At node b
`I_3 +(x+5-10)/2 = I_2 or 5/2 + ((x-5)/2) = I_2`
`x/2 = I_2`
At node c
`I_1 = I_2 + (x-0)/4`
`5/2 - x/4 = x/2 + x/4 or x= 5/2`
or `I_1 = 5/2 - 5/8 = 15/8 A` (current through upper conducting
wire)
And `I_2 = 5/4A` (current through 5V battery)
The current `(I_4)` in `2Omega` wire
`I_4 = ((5/2+5)-10)/2 = (5/2-5)/2 = -5/4A`
At node d: `I_5 - 5/4 = 5 or I_5 = 5+ 5/4 = 25/5A`
(current through 10 V battery)
Hence `I_6-I_5 = (x-0)/4 = ((5/2-0)/4)`
or `I_(6) - (25)/(4) = 5/8`
or `I_(6) = 5/8 + 25/4 = 55/8A`. (Current through lower conducting wire).