Discharging a capacitor through resistor and uncharged cap

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SUMMARY

This discussion focuses on analyzing the discharge of a capacitor through a resistor in an RC circuit after switching configurations. The initial charge on capacitor C1 is denoted as q0, and the problem involves determining the current through resistor R1 after switch S2 is closed. The solution utilizes Kirchhoff's Voltage Law (KVL) and the known behavior of RC circuits, specifically the exponential decay of current, to establish the relationship between initial and final conditions. The time constant for the circuit is crucial for solving the differential equation governing the current I(t).

PREREQUISITES
  • Understanding of RC circuit behavior
  • Familiarity with Kirchhoff's Voltage Law (KVL)
  • Knowledge of differential equations
  • Concept of time constants in electrical circuits
NEXT STEPS
  • Study the derivation of the exponential decay function in RC circuits
  • Learn how to apply Kirchhoff's Voltage Law in complex circuits
  • Explore the concept of time constants in various RC configurations
  • Investigate initial and steady-state conditions in electrical circuits
USEFUL FOR

Electrical engineering students, circuit designers, and anyone studying transient analysis in RC circuits will benefit from this discussion.

sdfanm16
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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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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.
 

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