Unformatted text preview: Inductive and Capacitive Transients – SUMMARY (Jackson: Ch 13(C), 17(L). Boylestad Ch 10(C), 11(L)) Changing current, i, and voltage, v, in an inductor or capacitor: L C Instantaneous: Transient Response timeframes: i/v Previous conditions t = t to 0 i v Exponential: Time period of interest t = 0+ to t (∞) t t = 0 (time when the circuit changes from L or C perspective Use x(t ) = X f − X f − Xi e ( ) −t τ , where Xf and Xi are the final and initial values during Th the period of interest, and τ is the time constant ( L R , RThC ) and RTh is the resistance “seen” by the inductor or capacitor again, during the period of interest. Determining Initial and Final Values: iL(t=0+) = iL(t=0) vL(t=0+): use old current(t=0) and new circuit(t=0+) and KVL vC(t=0+) = vC(t=0) For C iC(t=0+): use old voltage(t=0) and new circuit(t=0+) and KVL At steady‐state, the voltage across and inductor or the current through a capacitor is always 0 (vL(t=∞)=0V, iC(t=∞)=0A). For the final current in an inductor or the final voltage across a capacitor, use basic circuit analysis, remembering that at steady‐state(SS, t=∞), an inductor looks like a short and a capacitor looks like an open For L initial final LSS: CSS: Denard Lynch Oct 2008 ...
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- Spring '10
- Volt, rth, Denard Lynch, Transient Response timeframes, i/v Previous conditions