Second Order Resistor Capacitor Inductor (RCL) Series Circuits
Strings (SiPjAjk) = S7P4A41 Base Sequence = 12735 String Sequence = 12735 - 4 - 41
The circuit illustrated in figure 5.57 is a second order RCL circuit.
Vs = 12 V; C = 0.5 μF;
R1 = 31 kΩ; R2 = 22 kΩ
L = 0.9 mH.
The switch is closed at t = 0 after having been open for an extended period of time.
(a) The current through the inductor after the circuit has returned to steady state.
(b) The voltage across the capacitor after the circuit has returned to steady state.
(a) S7P4A41 (Linear Motion - Current Flowing Into Passive Elements). The motion of current flow in an electric circuit can be viewed as piece-wise-linear (current flow into a device) or looped (current flow in a circuit branch or the entire circuit). In a series connection, the piece-wise-linear current and looped current are the same. In a parallel connection, they are not. The looped current is stringed as S7P4A42 (Curved Motion).
(b) S7P3A32 (Force - Push).
(a) Pj Prblem of Interest is of type motion (Linear Motion).
At steady state:
Current through inductor = iL(∞); voltage across inductor = vL(∞) = 0;
Current through capacitor = iC(∞) = 0; voltage across capacitor = vC(∞)
Applying Kirchoff Voltage Law (KVL) to loop acdf we have:
V - R1iL(∞) - R2iL(∞) = 0 ---------(1)
So, 12 - (31 x 103)iL(∞) - (22 x 103)iL(∞) = 0;
So, iL(∞) = 12/(53 x 103) = 226 x 10-6) = 226 μA.
(b) Pj Problem of Interest is of type force (Force - Push).
At steady state, iC(∞) = 0;
So, vC(∞) = vR2(∞)
vR2(∞) = iL(∞)R2 = (22 x 10 3) x (226 x 10 -6) = 4.97 V.
So, vC(∞) = 4.97 V.
The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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