Final answer:
Kirchhoff's rules are used to find the currents I2 and I3 in a complex circuit. I2 is found to be -3.50 A, indicating an opposite direction to the assumed one, and I3 to be 8.25 A, the same as the assumed direction. The problem-solving involves the junction rule and loop rule because simple Ohm's law and series-parallel aren't enough.
Step-by-step explanation:
The student's question pertains to Kirchhoff's rules and their application in determining the direction and magnitude of currents in a circuit. To solve for the current labeled I, we would typically start by applying Kirchhoff's junction rule at a point (also known as a node) within the circuit, which states that the sum of currents entering the node must equal the sum of currents leaving the node. In tandem, Kirchhoff's loop rule can be applied, which states that the sum of potential differences (voltage) around any closed circuit loop must be zero.
Given the informational snippets, first, the value for I1 was substituted into an equation to find I2, yielding I2 = -3.50 A (indicating that the direction of current I2 is opposite to the assumed direction). Secondly, after substituting the value for I1 into another equation, we find that I3 = 8.25 A, suggesting that the direction of I3 is the same as the assumed direction. These values are resultant of utilizing both the junction and loop rules which are necessary because the circuit's complexity renders Ohm's law and series-parallel techniques insufficient.