Final answer:
It's not possible to solve for the voltages at nodes a. A and B or the current through the diode without additional information, like input voltages or directions of current flow.
Step-by-step explanation:
When analyzing circuits with ideal diodes, Kirchhoff's rules can be applied to determine the voltage at various nodes and the current flowing through components. The circuit in question involves resistors R1, R2, and R3 along with ideal diodes. To find the unknown parameters (voltages at nodes A and B, and the current through the diode), you would first apply Kirchhoff's junction rule at point A, which gives us the first equation I₁ = I₂ + I₃.
To find the voltages and currents in the upper and lower loops of the circuit, Kirchhoff's loop rule is used. This provides two more equations based on the sum of voltage drops and rises around each closed loop. Given that several parameters such as the values of R1, R2, R3, and the supplied voltages E1 and E2 are specified, one can solve these simultaneous equations to find the required electrical quantities.
With the given resistances R1 = 2 kΩ, R2 = 1 kΩ, and R3 = 3 kΩ, you would need more information such as input voltages to properly solve for VA, VB, and the current through the diodes. If additional details on voltages or direction of current flow were provided, one could then utilize Ohm's law, V = IR, along with the calculated voltages to deduce the current in the diodes.