Question

Two batteries and four resistors are connected as pictured below. Clearly label three unique currents within this circuit. Solve for all three currents. LW 212 8 V 312 4V 612 522

Answer 1

Given:

R1 = 2 Ω R2 = 3 Ω R3 = 6 Ω R4 = 5 Ω V1 = 4V V2 = 8V

Let us assume that $I_1$ flows to up through $V_1$ , $I_2$ flows up through
RE
and $I_3$ flows down through $V_2$

Applying Kirchchoff's Voltage Rule to left mesh in CW direction, we get

Applying KVL to right mesh in CW direction, we get

Applying Kirchchoff's Current Law to any of the junctions, we get

$I_1+I_2-I_3=0.........(3)$

Solving these three linear equations, we get

$I_1=0.741\ \text A\\ I_2=0.395\ \text A\\ I_3=1.14\ \text A$