find the emfs `epsilon_1 and epsilon_2` in the circuit in fig also find the potential difference of point b relative to point a.

Explanation

From the given current in the diagram, the curretn through
the middle branch of the circuit must be 1.00 A (the difference
between 2.00 A and (1.00A). Using Kirchhoff's rules and passing
counterclockwise around the top loop, we have
`20 - 1xx1+4xx1+1 - epsilon_(1) - 6xx1 = 0 or epsilon_(1) = 18V`
Now traveling around the external loop of the circuit, we have
`20 - 1xx1 - 1xx2 - epsilon_(2) - 2xx2 -6xx1 = 0 or epsilon_(2) = 7V`
and `V_(a) + 4 xx1 + 1 - epsilon_(1) = V_(b) or V_(b) - V_(a) = 5 -18 = -13V`