Circuit is attached© BrainMass Inc. brainmass.com September 22, 2018, 3:29 pm ad1c9bdddf - https://brainmass.com/physics/current-law/current-and-power-dissipation-573922
Let us assume current through R be I3 and comping out of battery of 12 V, i.e., all 3 currents are incident towards a junction.
E1 = 13 V
E2 = 14 V
E3 = 12 V
R1 = 1 ohm
R2 = 2 ohm
R = 3 ohm
At one of the two junctions, by Kirchhoff's current law (KCL),
I1 + I2 + I3 = 0 ...(1)
For closed ...
In a given electric circuit, by using Kirchhoff current and voltage law, currents are estimated in associated resistances. Also, power dissipation in the resistances are estimated.