Question

Current passing through 3 Ω resistance is(a) (14/3) A(b) 3 A(c) 2 A(d) (12/5) A

Answer 1

my calculation said answer is 2A i am not totaly sure

Acc. to me,

First divide Current

Suppose i1 current flow from 10V

and i2 from 4V   [from +ve to -ve]

At A

acc. to junction rule

outgoing current=incoming current

i1+i1=i1+i2

i1 come from 10V and i2 from 4V----incoming

i1+i2 current go out from A to B-----outgoing

and then current Divide again junction rule at B

i1+i2 is come from A to B----incoming

i2 go in 4V-----outgoing

and i1 go in 3 ohm----outgoing

Find current i1 and i2

just go from potential A and return to Potential A from another path [you know in current direction potential decreases and vice versa]

Vabca

Va-2(i1+i2)-3i +10=Va

Va can cancel then

2i1+2i2+3i1=10

5i1+2i2=10-------eqn1

Again from Va to Va

Vaba

Va-2(i1+i2)+4=Va

2i1+2i2=4

i1+i2=2------eqn2

From Eqn 1 and 2

i1=2 and i2=0

you see current i1 go in resistor of 3 ohm

then current is

current i1 value is 2 A

I hope it help