Question

A) In the circuit shown in the figure , find the magnitude of current in the upper branch.

B) Find the magnitude of current in the middle branch.

C) Find the magnitude of current in the lower branch.

D) What is the potential difference $V_{ab}$ of point relative to point ?

Answer 1

the kirchoff's loop eqns in upper loop is
-2Ia-10-3Ia+4Ib+5+Ib=0
=>5Ib-5Ia=5
=>Ia=Ib-1............(1)
for lower loop
-Ib-5-4Ib+10Ic=0
=>10Ic-5Ib=5
=>2Ic-Ib=1
=>Ib=2Ic-1.............(2)
also
Ia+Ib+Ic=0
=>Ib-1+Ib+Ic=0
=>2Ib+Ic=1
=>4Ic-2+Ic=1
=>5Ic=3
=>Ic=3/5=0.6
so Ib=2Ic-1=0.2
Ia=Ib-1=-0.8

a)magnitude of current in upper branch=|Ia|=0.8 A
b)magnitude of current in middle branch=|Ib|=0.2 A
c)magnitude of current in lower branch=|Ic|=0.6 A
d)between a and b
Va-3Ia+4Ib-Vb=0
=>Va-Vb=3Ia-4Ib=-3x0.8-4x0.2=-2.4-0.8=-3.2 V

Answer 2