\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Consider a simple RL circuit with a resistor \(R\), an inductor \(L\), and a constant voltage source \(E\). The current \(I(t)\) in the circuit is governed by the first-order differential equation:$$L\frac{dI}{dt} + RI = E$$
  1. State the initial condition \(I(0)\) if the circuit is switched on at time \(t=0\).
  2. Verify that the general solution to this equation is \(I(t) = \frac{E}{R} + Ae^{-\frac{R}{L}t}\), where A is an arbitrary constant.
  3. Use the initial condition to find the particular solution for the current in the circuit.

Capture an image of your work. AI teacher feedback takes approximately 10 seconds.