Electric Circuits and Networks

10.9 SERIES RL CIRCUIT WITH EXPONENTIAL INPUTS

We take up the study of a zero-state response of series RL circuit for exponential inputs and sinusoidal inputs in this section. We do not worry about the zero-input response anymore since we know that it is I₀e^–t/τ, where I₀ is the initial current specified at t = 0^–. The total response is found by adding zero-input response and zero-state response together.

We permit exponential inputs of the form e^stu(t) in this section, where s can be a complex number s = –σ + jω, where σ and ω are two real numbers. The reason for generalising the exponential input in this manner will be clear soon. We put a negative sign behind σ since we want the real part of s to be negative when σ is positive. This signal ...