Calculating the Steady State Value of Vc After Opening a Switch in a RC Circuit

In summary, the question is asking for the steady-state value of Vc after a switch opens and the time it takes for Vc to be within 1 percent of its steady-state value. The solution involves understanding the behavior of the capacitor as an open circuit in parallel with the resistor. Using the equation Vc=IR, the steady-state value of Vc is found to be 10 volts.
  • #1
compEng
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Please Help me with this problem or with understanding it. Thank you!

Homework Statement


What is the stead-state value of Vc after the switch opens? Determine how long it takes after the switch opens before Vc is within 1 percent of its stead-state value.

Homework Equations



Vc = Vie-t/RC

The Attempt at a Solution

 

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  • #2
It doesn't look like you've attempted the solution. but I'll give you some tips.
when the system is in a steady state the capacitor acts as an open circuit (ie: all the current goes through the 1k resistor.)

what is the voltage across the 1k resistor at steady state: 1x10^3 x 10x10^-3
what do you know about elements connected in parallel.

I've made this part really obvious for you. finish the first part and attempt the second part and I'll give you some more help if you need it.

Good luck
 
  • #3
okay i think I figured it out.

Because the capitor becomes an open circuit, and because it is in parrelel with the resistor it begins to imitate a Norton Equivilant circuit. and Vc=IR

Vc= 10 * 10-3 * 103 = 10

thank you!
 

FAQ: Calculating the Steady State Value of Vc After Opening a Switch in a RC Circuit

1. What is the Steady State value of V_c?

The Steady State value of V_c is the equilibrium value of a variable V_c in a system, where the rate of change of V_c is equal to zero. This means that the value of V_c remains constant over time.

2. Why is the Steady State value of V_c important in scientific research?

The Steady State value of V_c is important because it can provide insights into the behavior and stability of a system. It can also help determine the optimal conditions for a process or the long-term effects of a particular variable.

3. How is the Steady State value of V_c calculated?

The Steady State value of V_c is typically calculated using mathematical models and equations that describe the relationship between V_c and other variables in the system. This can involve solving differential equations or using simulation techniques.

4. Can the Steady State value of V_c change over time?

In most systems, the Steady State value of V_c remains constant. However, certain factors such as external disturbances or changes in the system's parameters can cause the value to change over time. In these cases, the system may reach a new Steady State value after a period of adjustment.

5. How is the Steady State value of V_c different from other equilibrium points?

The Steady State value of V_c is a specific type of equilibrium point where the rate of change is zero. Other equilibrium points, such as unstable or stable points, have different characteristics and can have different implications for the behavior of a system.

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