ECE CHAPTER 4

# ECE CHAPTER 4 - Transients Transients the time-varying...

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Transients - Transients: the time-varying currents and voltages resulting from the sudden application of sources, usually due to switching First-Order RC Circuits - Contain independent dc sources, resistances, and a single capacitance Discharge of a Capacitance through a Resistance - Figure 4.1(a) - C dv c (t)/dt +v c (t)/R = 0 - Solve: v c (t) =V i e -t/RC - The voltage across the capacitor cannot change instantaneously when the switch closes - Time constant: τ = RC - In one time constant, the voltage decays by the factor e -1 Charging a Capacitance from a DC Source through a Resistance - Figure 4.3 - C dv c (t)/dt +(v c (t) – V s )/R = 0 - Solve: v c (t) =V s – V s e -t/RC - The second te\rm on the right-hand side is called the transient response , which eventually decays to negligible values - The first term on the right-hand side is called the steady-state response (or forced response ) - V s is the final voltage value DC Steady State - For steady-state conditions with dc sources, capacitances behave as open circuits

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ECE CHAPTER 4 - Transients Transients the time-varying...

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