Consider the RL circuit shown in Figure 8.1a, consisting of a resistance \(R\) and an inductance \(L\). The initial current is \(i(0)=i_{0}\). Assuming the applied voltage \(v_{a}\) is modeled as a step function with magnitude \(V\), find the zero-input, zero-state, and steady-state responses.

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R FIGURE 8.1 (a) mm (a) RL circuit and (b) response to a step input. i(0) = io V Steady-state current R 0 (b) Zero-state response Zero-input response t