Capacitor charge time on DC RLC circuit

In summary, the question involves a series circuit with a DC source, inductor, resistor, and capacitor. The DC source has a voltage of 220 V, the capacitor has a capacitance of 10F, the inductor has an inductance of 5H, and the resistor has a resistance of 22 ohm. The question asks for the charge time of the capacitor when it becomes fully charged and starts acting like an open circuit. The attempt at a solution involved using KVL and equations for voltage and current, but the resulting differential equation could not be solved.
  • #1
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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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  • #2
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?
 

What is a DC RLC circuit?

A DC RLC circuit is an electrical circuit that consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series with a direct current (DC) power source. This type of circuit is used to study the behavior of electrical energy in a closed loop.

What is a capacitor?

A capacitor is an electronic component that stores electrical energy in the form of an electric field. It consists of two conductive plates separated by an insulating material, known as a dielectric. When a voltage is applied to the plates, it causes the buildup of positive and negative charges, creating an electric potential difference.

How does a capacitor charge on a DC RLC circuit?

In a DC RLC circuit, a capacitor charges when a voltage is applied across its plates. Initially, the capacitor acts like a short circuit, allowing current to flow through it. As the capacitor charges, the current decreases, and the voltage across the capacitor increases until it reaches the same value as the applied voltage.

What factors affect the charge time of a capacitor on a DC RLC circuit?

The charge time of a capacitor on a DC RLC circuit is affected by several factors, including the capacitance of the capacitor, the resistance of the circuit, and the inductance of the inductor. A larger capacitance will result in a longer charge time, while a higher resistance or inductance will decrease the charge time.

How can the charge time of a capacitor on a DC RLC circuit be calculated?

The charge time of a capacitor on a DC RLC circuit can be calculated using the equation t = RC, where t is the charge time in seconds, R is the resistance in ohms, and C is the capacitance in farads. This equation assumes an ideal circuit without any losses or external factors influencing the charge time.

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