Capacitor Voltage Homework: Vo(0), v(infinity), & R

In summary, the student is trying to solve a problem involving the current flowing through an inductor, but does not mention i(infinity) once. They are also unclear about the current through the inductor at steady state.
  • #1
princejan7
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0

Homework Statement



http://postimg.org/image/4m0huqxpj/

Homework Equations



v(t)=v(infinity)+ [v(0) - v(infinity)]^e(-t/RC)

The Attempt at a Solution

I found Vo(0) to be 8V, but I'm not sure about about v(infinity) and R

If the switch is at B and the capacitor is an open circuit at steady state, then shouldn't the resistance be the addition of the parallel combination of 40k and 30k and the 20k
however, the solution for R is given as 12and for v(infinity), I don't know know what to do
 
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  • #2
When the switch moves to position B the 40 k resistor will have one end open, so no current can flow through it and it will play no further role in the circuit.

For v, remove the capacitor from the circuit and determine the potential across the points where it was connected.
 
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  • #3
gneill said:
When the switch moves to position B the 40 k resistor will have one end open, so no current can flow through it and it will play no further role in the circuit.

For v, remove the capacitor from the circuit and determine the potential across the points where it was connected.

thanks, I have another question

http://postimg.org/image/m6c1rf60h/ [Broken]

why is there no mention of i(infinity) for this?
is the current through the inductor zero at steady state with the switch closed?


i(t)=i(infinity)+ [i(0) - i(infinity)]^e(-Lt/R)
 
Last edited by a moderator:
  • #4
The inductor current falls away, becoming 0 at t=∞

The switch directs to ground all current from the battery, so the battery has no influence over the inductor once the switch closes.
 
  • #5
princejan7 said:
thanks, I have another question

http://postimg.org/image/m6c1rf60h/ [Broken]

why is there no mention of i(infinity) for this?
is the current through the inductor zero at steady state with the switch closed?


i(t)=i(infinity)+ [i(0) - i(infinity)]^e(-Lt/R)

For a NEW question, why not make a NEW thread? Did you solve the problem of the current thread?
 
Last edited by a moderator:

1. What is Vo(0)?

Vo(0) is the initial voltage across the capacitor at time t=0. It is the voltage that is present on the capacitor before it begins to charge or discharge.

2. What is v(infinity)?

v(infinity) is the final voltage across the capacitor after it has fully charged or discharged. It is the voltage that the capacitor will reach when it is fully stabilized.

3. How is Vo(0) related to v(infinity)?

Vo(0) is the initial voltage on the capacitor and v(infinity) is the final voltage on the capacitor. The relationship between these two values depends on the circuit and the values of the components used.

4. How does the value of R affect the capacitor voltage?

The value of R, or resistance, in a circuit affects the charging and discharging rate of the capacitor. A higher resistance will result in a slower rate of change in capacitor voltage, while a lower resistance will result in a faster rate of change.

5. What other factors can affect the capacitor voltage?

Apart from the value of R, the capacitor voltage can also be affected by the capacitance of the capacitor, the voltage source connected to the circuit, and any other components or external factors that may impact the circuit's behavior.

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