# RLC Circuit Analysis -- Two sources and two switches

• wcjy
In summary, the conversation discusses a working that involves a capacitor and a switch. It is mentioned that the capacitor acts as an open circuit when t < 0 and when t = ∞, and the time constant is calculated to be 0.2 seconds. The equation for V(t) is also provided and it is determined that α = 5, β = 4, and γ = -5. The expert acknowledges that the approach and results look good, but points out a sign error in some of the exponents. The expert also praises the reasoning and simple approach used to solve the problem, but notes that it relies on the knowledge of the solution to the series RC differential equation.
wcjy
Homework Statement
Given the following circuit with the source voltages V1=9(V) and V2=5(V). Switch 1 has been connected to A and switch 2 has been closed for a long time. At t=0, switch 1 is connected to B, and switch 2 is open. Find the constants α, β, and γ in the expression of the voltage v(t) through the capacitor

V(t) = α + βe^(γt) V
Relevant Equations
$$V(t) = V( ∞) + [V(0) - V( ∞)] e ^ {\frac{t}{T}}$$
Hello, this is my working. My professor did not give any answer key, and thus can I check if I approach the question correctly, and also check if my answer is correct at the same time.

When t < 0, capacitor acts as open circuit,
$$V(0-) = V(0+) = 9V$$

When t = infinity,
$$V( ∞) = 5V$$ (because switch is now connected to B, and capacitor acts as open circuit when t = ∞)

Time Constant, $$T = RC = 2 * 100 * 10^{-3} = 0.2 s$$

When t > 0,
$$V(t) = V( ∞) + [V(0) - V( ∞)] e ^ {\frac{t}{T}}$$
$$V(t) = 5 + [9 - 5] e^{\frac{-t}{0.2}}$$
$$V(t) = 5 + 4e^{-5t}$$

Therefore,
α = 5,
β = 4
γ = -5

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Your approach and results look good.

wcjy
Looks good. You have a sign error in some of your exponents.
Your reasoning is great; the simple approach. There are much harder ways to solve this that you successfully avoided. Of course it does rely on you already knowing the solution to the series RC differential equation (i.e. time constant and exponentials), but that seems reasonable since they gave you the form of the answer.

wcjy
Thank You Very Much!

berkeman

## 1. What is an RLC circuit?

An RLC circuit is an electrical circuit that contains a resistor (R), an inductor (L), and a capacitor (C). These three components are connected in series or parallel and form a closed loop for the flow of current.

## 2. How do two sources and two switches affect an RLC circuit?

Having two sources and two switches in an RLC circuit allows for more control over the flow of current. The sources can provide different voltages, and the switches can open or close the circuit, changing the path of the current.

## 3. What is the purpose of analyzing an RLC circuit with two sources and two switches?

Analyzing an RLC circuit with two sources and two switches helps to understand the behavior of the circuit and how it responds to different inputs. It can also be used to calculate the values of current, voltage, and impedance at different points in the circuit.

## 4. How do you solve an RLC circuit with two sources and two switches?

To solve an RLC circuit with two sources and two switches, you can use Kirchhoff's laws and Ohm's law to create a system of equations. Then, you can use algebraic methods or circuit analysis techniques, such as nodal or mesh analysis, to solve for the unknown variables.

## 5. What are some real-world applications of RLC circuit analysis with two sources and two switches?

RLC circuit analysis with two sources and two switches is commonly used in electronic devices, such as radios, amplifiers, and filters. It is also used in power systems to analyze and optimize the flow of electricity. Additionally, it is used in research and development of new technologies, such as wireless power transfer systems.

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