Final answer:
The student's question involves the analysis of RL circuits in electrical engineering, calculating time constants, initial and final currents, and voltages at specific times using transient analysis formulas.
Step-by-step explanation:
The student is asking for help with the dynamics of RL circuits, where L is the inductance and R is the resistance in the circuit. The task involves finding the time constant, initial current, and final current through the resistor, as well as the current and voltages across components at specified times. It involves using the knowledge of electrical engineering, specifically focusing on the transient analysis of RL circuits.
The key steps typically include:
Determining the time constant (τ = L/R) which dictates how quickly the circuit responds.
Calculating the initial current I(0) using Ohm's law I = ε/R immediately after the switch is closed.
Finding the final current I(∞) which is determined by the steady-state condition of the circuit.
Using the formula I(t) = I(0) + [I(∞) - I(0)](1 - e-t/τ) to find the current at any time t.
The voltages across the inductor and resistor can be found using the relationships VL(t) = L(dI/dt) and VR(t) = I(t)R respectively.