Capacitor charge time on DC RLC circuit

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SUMMARY

The discussion focuses on calculating the charge time of a capacitor in a DC RLC circuit consisting of a 220 V DC source, a 10 F capacitor, a 5 H inductor, and a 22 ohm resistor. The initial voltage across the capacitor is 50 V. The user derived a differential equation for the capacitor voltage (Vc) using Kirchhoff's Voltage Law (KVL) and the relationships for inductance and capacitance but encountered difficulties in progressing further with the solution. The key takeaway is the understanding of the circuit's behavior as the capacitor charges and eventually acts as an open circuit.

PREREQUISITES
  • Understanding of Kirchhoff's Voltage Law (KVL)
  • Familiarity with differential equations
  • Knowledge of RLC circuit dynamics
  • Concept of capacitor charging in DC circuits
NEXT STEPS
  • Study the solution of first-order differential equations in RLC circuits
  • Learn about the time constant in RC circuits and its implications
  • Explore the behavior of capacitors in series and parallel configurations
  • Investigate the transient response of RLC circuits to DC sources
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Electrical engineering students, circuit designers, and anyone interested in analyzing RLC circuits and capacitor charging behavior in DC applications.

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Homework Statement



Inductor, resistor and a capacitor is connected to a DC source in series.
DC source is 220 V
Capacitance is 10F
Inductance 5H
Resistor 22 ohm
Vc(0) = 50V

Question is asking for the charge time of the capacitor, when it gets charged fully and then it starts to act like open circuit (If I'm not mistaken it must be act like short until gets fully charged and then acts like open circuit)

Homework Equations





The Attempt at a Solution



I wrote down the KVL and equation. And then replaced the VL with L.dI/dt and I=C.dVc/dt
Finally I ended up with a dif. equation on Vc.

However, I couldn't proceed any further.
 
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zoom1 said:


The Attempt at a Solution



I wrote down the KVL and equation. And then replaced the VL with L.dI/dt and I=C.dVc/dt
Finally I ended up with a dif. equation on Vc.

However, I couldn't proceed any further.


Why not? What was your equation?
 

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