Final answer:
To determine the current at t=1s and t=4s in the given circuit, we can use Kirchhoff's rules. By applying the junction and loop rules, equations can be written and solved to find the currents I1, I2, and I3. Given the circuit values, the currents at the specified times can be calculated.
Step-by-step explanation:
In order to determine the current at t=1s and t=4s in the given circuit, we can use Kirchhoff's rules. Kirchhoff's junction rule states that the sum of currents entering a junction is equal to the sum of currents leaving the junction. Kirchhoff's loop rule states that the sum of voltage drops around any closed loop in a circuit is equal to the sum of emf (electromotive force) in that loop.
By applying Kirchhoff's rules to the circuit, we can write equations based on the junction rule at point A and loop rules in the upper and lower loops. Solving these equations will allow us to find the currents I1, I2, and I3. Given the values for R₁, R₂, R₃, r₁, r₂, E₁, and E₂, we can calculate the currents at t=1s and t=4s.