Deriving expression for capacitor voltage

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SUMMARY

The discussion focuses on deriving the expression for capacitor voltage, vC(t), in a first-order dynamic circuit with a voltage source vs(t) = 10 V and an initial condition vC(0) = 2 V. Participants emphasize applying Kirchhoff's Voltage Law (KVL) to establish the relationship between the voltage source and the capacitor. The solution involves treating the initial voltage condition as a step input, allowing for the calculation of vC(t) using differential equations and integration techniques.

PREREQUISITES
  • Understanding of Kirchhoff's Voltage Law (KVL)
  • Familiarity with first-order dynamic circuits
  • Knowledge of differential equations
  • Ability to perform definite integrals
NEXT STEPS
  • Study the application of Kirchhoff's Voltage Law in circuit analysis
  • Learn about solving first-order differential equations in electrical circuits
  • Explore the concept of initial conditions in dynamic systems
  • Research techniques for integrating step functions in circuit analysis
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing dynamic circuits and capacitor behavior.

Studious_stud
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Homework Statement


t98aa0.jpg


For the following circuit, obtain an expression for the capacitor
voltage, vC(t), for time, t (greater than or equal to) 0 if vs(t) = 10 V and vC(0) = 2 V.

Homework Equations



KVL
Definite integrals, differentiation etc

The Attempt at a Solution



Right so I can do this for a first order dynamic circuit (one with only one capacitor and one inductor) but this one is throwing me off.

I'd imagine you'd start by applying KVL to obtain an expression for the voltage source?

After that I'm kinda lost

Any help would be really appreciated thanks
 
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Studious_stud said:

Homework Statement


t98aa0.jpg


For the following circuit, obtain an expression for the capacitor
voltage, vC(t), for time, t (greater than or equal to) 0 if vs(t) = 10 V and vC(0) = 2 V.

Homework Equations



KVL
Definite integrals, differentiation etc

The Attempt at a Solution



Right so I can do this for a first order dynamic circuit (one with only one capacitor and one inductor) but this one is throwing me off.

I'd imagine you'd start by applying KVL to obtain an expression for the voltage source?

After that I'm kinda lost

Any help would be really appreciated thanks

It looks like you just solve the circuit like the Vc(0) were zero, with a step input voltage at t=0 from the voltage source, but instead use Vc(0) = 2V as the initial condition instead. What is the issue?
 

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