Final answer:
To find the current I(t) in the RL circuit with a given voltage source E(t) = 10 - 2t volts, a resistor (R = 0.1 Ohms), and an inductor (L = 1H), we must use the differential equation V(t) = L(dI/dt) + IR with the initial condition I(0) = 0 and solve it using appropriate methods such as integrating factors or Laplace transforms.
Step-by-step explanation:
The student is working with an RL circuit involving a series connection of a resistor and an inductor connected to a time-varying voltage source. To find an expression for the current I(t) at time t, we need to establish the relevant differential equation for circuits with both resistance and inductance.
Starting with the given voltage source E(t) = 10 - 2t volts and using L to denote inductance and R to denote resistance, we can set up the differential equation. We then have:
V(t) = L(dI/dt) + IR,
where V(t) is the applied voltage and I is the current. Since we are given that there is no current at time t=0, we have an initial condition I(0) = 0. Solving this differential equation involves finding the particular solution given the form of E(t).
Unfortunately, the provided handout snippets do not contain the full equations or methods needed to solve the problem. However, it is commonly solved using an integrating factor or by employing Laplace transforms, resulting in an expression of current as a function of time that typically includes exponential factors representing the transient behavior of the RL circuit.