Calculating steady-state values in series RC circuit

In summary: Also, what voltage will appear across the resistor?In summary, the problem is asking for the steady state values of the current, voltage V1, and voltage V2 in a series circuit with a 1.2 kΩ resistor, a 10V source, and a 100 μF capacitor. The time constant of the circuit is 0.12 seconds and after 0.6 seconds (5 time constants), the capacitor will reach its steady state voltage. The current in the circuit will be 8.3 mA and the voltage across the capacitor will be 10V, while the voltage across the resistor will be 0V.
  • #1
itlivesthere
4
0

Homework Statement


Calculate the steady state values of the current, voltages V1 and V2 (defined by a period of time greater than five time constants). (Circuit in ASCII below).
+ V1 -
_________Res (1.2 kΩ)___________
| I => |
| | +
| + |
E 10V Cap (100 μF) V2
| - |
| | -
|------------------------------------------|
GND

Homework Equations


τ=RC, E=IR, V= Vsource(1-e^-t/RC)

The Attempt at a Solution


I'm a novice at electrical/electronics engineering, but I'm eager to learn all I can. Correct me if I'm wrong with the following:
I determined the time constant of this circuit is .12 seconds. As I understand correctly, it takes approximately five time constants for a capacitor to charge up to its steady-state voltage, which in this case equates to .6 seconds.
The current after it crosses the 1.2 kΩ resistor is calculated as 8.3 mA.
I'm very much stuck at this point... any advice?
 
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  • #2
Hi itlivesthere, welcome to PF.

You might want to put anything that depends upon horizontal spacing of characters (like ascii circuit diagrams) within [.code] [./code] delimiters (without the "." in each), and use a fixed width font to build the picture. You'll probably want to build the picture in a separate editor in which you can change the font accordingly, then cut & paste the result between the "code" delimiters.

Alternatively, upload a picture of your circuit, either drawn in a graphics program or snipped from a document. Here's an example showing what I think your circuit looks like:

attachment.php?attachmentid=41004&stc=1&d=1321543834.jpg


Now, on to your question. First you should recognize that this is a series circuit; all the components are connected end-to-end in a loop. In a series circuit the same current with the same value everywhere flows through each of the components. At steady state the current will be some constant value (and zero is a perfectly good value, too!). You stated your understanding that after some long time has passed (where engineers take "a long time" to mean more than 5 time constants!) that the capacitor will finish charging. What voltage will appear across the capacitor then?
 

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1. How do you calculate the steady-state voltage in a series RC circuit?

In order to calculate the steady-state voltage in a series RC circuit, you can use the formula V = V0 * e-t/RC, where V0 is the initial voltage, t is time, R is the resistance, and C is the capacitance.

2. What is the significance of the time constant in a series RC circuit?

The time constant, represented by the symbol τ, is the amount of time it takes for the voltage in a series RC circuit to reach 63.2% of its steady-state value. It is a measure of how quickly the circuit reaches equilibrium.

3. How does the resistance affect the steady-state voltage in a series RC circuit?

The resistance in a series RC circuit affects the steady-state voltage by determining how quickly the voltage reaches its final value. A higher resistance will result in a longer time constant and a slower convergence to the steady-state voltage.

4. Can you calculate the steady-state voltage in a series RC circuit without knowing the initial voltage?

No, the initial voltage is a necessary component in the formula for calculating the steady-state voltage. Without this value, it is not possible to accurately determine the final voltage in the circuit.

5. How do you know when a series RC circuit has reached its steady-state?

A series RC circuit is considered to have reached its steady-state when the voltage across the capacitor has stopped changing over time. This is typically when the voltage has reached 99% of its final value, but it can also be determined by monitoring the voltage over time and observing when it levels off.

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