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Transients
 Transients: the timevarying currents and voltages resulting from the sudden application
of sources, usually due to switching
FirstOrder
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 righthand side is called the
transient response
, which
eventually decays to negligible values
 The first term on the righthand side is called the
steadystate response
(or
forced response
)

V
s
is the final voltage value
DC Steady State

For steadystate conditions with dc sources, capacitances behave as open circuits
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 Spring '08
 BEST
 Volt

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