RLC Circuit Analysis -- Two sources and two switches

AI Thread Summary
The discussion focuses on analyzing an RLC circuit with two sources and switches, confirming the correctness of the approach and calculations. The capacitor behaves as an open circuit for t < 0 and t = ∞, with voltage values of 9V and 5V respectively. The time constant is calculated as T = 0.2 seconds, leading to the voltage equation V(t) = 5 + 4e^{-5t}. Feedback indicates that the approach and reasoning are sound, though there is a sign error in some exponents. Overall, the analysis demonstrates a solid understanding of the series RC differential equation.
wcjy
Messages
73
Reaction score
10
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
 

Attachments

  • 1615635237437.png
    1615635237437.png
    79.7 KB · Views: 227
Last edited by a moderator:
Physics news on Phys.org
Your approach and results look good.
 
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.
 
Thank You Very Much!
 
Thread 'Minimum mass of a block'
Here we know that if block B is going to move up or just be at the verge of moving up ##Mg \sin \theta ## will act downwards and maximum static friction will act downwards ## \mu Mg \cos \theta ## Now what im confused by is how will we know " how quickly" block B reaches its maximum static friction value without any numbers, the suggested solution says that when block A is at its maximum extension, then block B will start to move up but with a certain set of values couldn't block A reach...
TL;DR Summary: Find Electric field due to charges between 2 parallel infinite planes using Gauss law at any point Here's the diagram. We have a uniform p (rho) density of charges between 2 infinite planes in the cartesian coordinates system. I used a cube of thickness a that spans from z=-a/2 to z=a/2 as a Gaussian surface, each side of the cube has area A. I know that the field depends only on z since there is translational invariance in x and y directions because the planes are...
Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'
Figure 1 Overall Structure Diagram Figure 2: Top view of the piston when it is cylindrical A circular opening is created at a height of 5 meters above the water surface. Inside this opening is a sleeve-type piston with a cross-sectional area of 1 square meter. The piston is pulled to the right at a constant speed. The pulling force is(Figure 2): F = ρshg = 1000 × 1 × 5 × 10 = 50,000 N. Figure 3: Modifying the structure to incorporate a fixed internal piston When I modify the piston...
Back
Top