8.6 Step Response of a Parallel RLC Circuit

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Last updated 8:23 PM on 5/11/26
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The Step Response of a Parallel RLC Circuit

A parallel RLC circuit with a step response will be initially disconnected from a current source until it is connected at t = 0+.

From there, we apply KCL at the nodes to acquire our equations.

<p>A parallel RLC circuit with a step response will be initially disconnected from a current source until it is connected at t = 0+.</p><p></p><p>From there, we apply KCL at the nodes to acquire our equations. </p>
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Final Current Response for a Step-Response Parallel RLC Circuit

Like with all previous cases, the final response of the current through the inductor in a series of parallel RLC elements is given by the sum of the transient response and the steady-state value.

<p>Like with all previous cases, the final response of the current through the inductor in a series of parallel RLC elements is given by the sum of the transient response and the steady-state value. </p><p></p><p></p>
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Auxiliary Equation/Initial Conditions

We need three forms of information to solve for the coefficients of our current response function:

  1. V(0)

    1. The initial capacitor voltage at t = 0 (steady-state conditions)

  2. I(0)

    1. The initial inductor current at t = 0 (steady-state conditions)

  3. The Differential Term

    1. This time, we utilize the voltage-inductor relationship (since we are solving for the inductor’s current after all, same as how we use the current-capacitor relationship to solve for the capacitor’s voltage).

<p>We need three forms of information to solve for the coefficients of our current response function: </p><p></p><ol><li><p>V(0)</p><ol><li><p>The initial capacitor voltage at t = 0 (steady-state conditions)</p></li></ol></li><li><p>I(0)</p><ol><li><p>The initial inductor current at t = 0 (steady-state conditions)</p></li></ol></li><li><p>The Differential Term</p><ol><li><p>This time, we utilize the voltage-inductor relationship (since we are solving for the inductor’s current after all, same as how we use the current-capacitor relationship to solve for the capacitor’s voltage).</p></li><li><p></p></li></ol></li></ol><p></p>
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