Circuit Analysis: Equation Derivation Help

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SUMMARY

The discussion focuses on deriving equations for capacitor voltage in a circuit analysis context, specifically starting from the equation Vc(t) = 5(1-e^(-t/T)). The goal is to arrive at two specific equations for a 5 V square wave with a 50% duty cycle when T > 1/10f. The derived equations are Vc(t) = 5 - (5 / (1+e^(-1/2*f * T))) * e^(-t/T) and Vc(t) = (5 / (1+e^(-1/2*f * T))) * e^(-t/T). The discussion emphasizes the importance of demonstrating effort in problem-solving before seeking assistance.

PREREQUISITES
  • Understanding of capacitor charging equations in circuit analysis
  • Familiarity with exponential functions and their properties
  • Knowledge of square wave characteristics and duty cycles
  • Basic skills in algebraic manipulation of equations
NEXT STEPS
  • Study the derivation of capacitor voltage equations in RC circuits
  • Learn about the impact of duty cycle on capacitor behavior in square wave applications
  • Explore the use of Laplace transforms in circuit analysis
  • Investigate the effects of varying time constants (T) on circuit response
USEFUL FOR

This discussion is beneficial for electrical engineering students, circuit designers, and anyone involved in analyzing transient responses in RC circuits.

frankkk
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I am trying to solve a homework problem. I need some help to get going in the right direction if possible. My equation I am starting with is:

Vc(t) = 5(1-e^(-t/T))

and I have to end up with these two equations:
If T > 1/10f then for a 5 V square wave with a 50% duty cycle, the capacitor voltage is given by

Vc(t) = 5 - (5 / 1+e^(-1/2*f * T)) * e^(-t/T)

and

Vc(t) = (5 / 1+e^(-1/2*f * T)) * e^(-t/T)

Thanks!
 
Last edited:
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Frankkk, we can't help you unless you show some effort first. Please read our posting guidelines for homework. Also read the sticky thread at the top of this subforum.
 

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