Final answer:
The student's question involves analyzing a circuit using Kirchhoff's rules to calculate the currents through different resistors. The approach includes applying Kirchhoff's junction and loop rules to find three independent equations to solve for the unknown currents I1, I2, and I3, and determining the direction of current flow.
Step-by-step explanation:
The question is about analyzing a circuit using Kirchhoff's rules, specifically the junction rule and the loop rule. Given that the initial current is 26 mA, the calculations to find the current I1, I2, and I3 across various resistors are based on applying these rules at different points and loops of the circuit. We can write the equations based on Kirchhoff's junction rule at a given point (typically labeled 'A'), which allows us to understand how current flows into and out of that junction. For the loop rule, we can write equations for the upper and lower loops, which helps in calculating voltage differences around the loops. Lastly, we substitute the values for the resistances and emfs given, use algebra to solve for the currents I1, I2, and I3, and interpret signs to determine the correct direction of current flow.
For example, the equation I2 = 6 - 2I1 might be part of applying Kirchhoff's loop rule to the upper loop, where the value of 6 might represent the summed potential differences across batteries or resistors. If I2 is calculated to be negative, like -3.50 A, this indicates that the assumed direction for I2 is opposite to the actual direction of current flow in the circuit.
Lastly, substituting the value for I1 in equations related to other currents, such as I3, helps in finding the value of all currents involved. For instance, if I3 = 22.5 - 3I1, and I1 has been previously determined, we solve for I3. In this example, it happens to be 8.25 A, which confirms the strength of the current in that part of the circuit.