Discharging a capacitor through resistor and uncharged cap

In summary, the problem involves finding the current on r1 in a circuit with v0 c1c2 r1, where switch 1 is closed for a long time and then opened at t=0 while switch 2 remains closed. The approach is to use Kirchhoff's Voltage Law and known boundary conditions to solve for the unknown constants and determine the initial and final currents, which can then be used to calculate the current at any time using the behavior of an RC circuit.
  • #1
sdfanm16
3
0

Homework Statement



Given v0 c1c2 r1 need to find the current on r1 picture
New Document(16)-page-002.jpg

switch 1 is closed for long time and on t=0 opened and switch 2 is closed

Homework Equations

The Attempt at a Solution


in the attached file
New Document(16)-page-001.jpg

i was trying to use kvl assuming that q0(charge on cap before opening switch 1) is v0 adn the sum of q1 and q2 (the charge after switch 2 is closed) is equal to q0
how to find cons c and I(t)?
 
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  • #2
Usually one uses known boundary conditions (initial, steady state) to solve for the unknown constants, plugging the known conditions into the general solution of the differential equation.

For this problem it might be easier to just look at the initial and final conditions and "connect" them with the known behavior of an RC circuit. That is, if you can determine the initial current that flows the instant after the switch S2 is closed and the final current at steady state, you know that the current must follow an exponential decay between those states. You've already determined the time constant, so the rest will be straight forward.
 

Related to Discharging a capacitor through resistor and uncharged cap

1. What is the purpose of discharging a capacitor through a resistor and uncharged capacitor?

The purpose of discharging a capacitor through a resistor and uncharged capacitor is to remove any residual charge from the capacitor. This is important in order to safely handle the capacitor and to prepare it for future use.

2. How does discharging a capacitor through a resistor and uncharged capacitor work?

When a charged capacitor is connected to a resistor and an uncharged capacitor in series, the resistor acts as a current limiter and slows down the discharge process. The uncharged capacitor acts as a "sink" for the charge, allowing it to dissipate evenly and completely. This allows the capacitor to discharge safely without causing damage.

3. Can you discharge a capacitor through a resistor without using an uncharged capacitor?

Yes, it is possible to discharge a capacitor through a resistor without using an uncharged capacitor. However, this method may not fully dissipate the charge and can result in a dangerous residual charge remaining in the capacitor.

4. Is discharging a capacitor through a resistor and uncharged capacitor necessary?

In most cases, it is recommended to discharge a capacitor through a resistor and uncharged capacitor in order to safely handle and store the capacitor. However, if the charge is low and the capacitor is not being handled, discharging may not be necessary.

5. How long does it take to discharge a capacitor through a resistor and uncharged capacitor?

The time it takes to discharge a capacitor through a resistor and uncharged capacitor depends on the capacitance and initial charge of the capacitor, as well as the resistance of the resistor. It can take anywhere from a few seconds to several minutes for the capacitor to fully discharge.

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