Question

Find the emfs ${\epsilon }_1$ and ${\epsilon }_2$ in the circuit in Figure. Also find the potential difference of point $b$ relative to point $a$.

Answer 1

From the given currents in the diagram, the current through the middle branch of the circuit must be 1.00 A (the difference between 2.00 A and 1 .00 A). Using Kirchhoff's rules and passing counterclockwise around the top loop, we have
$20-1\times 1+4\times 1+1\times 1-{\epsilon }_1-6\times 1=0or{\epsilon }_1=18V$
Now traveling around the external loop of the circuit, we have
$20-1\times 1-1\times 2-{\epsilon }_2-2\times 2-6\times 1=0or{\epsilon }_2=7V$
and $V_a+4\times 1+1\times 1-{\epsilon }_1=V_{b}or{V}_b-V_a=5-18=-13V$