Chapter 4 TRANSIENTS
4.1
FirstOrder
RC
circuits
Discharge of a Capacitance through a Resistance
Figure 4.1 shows a fluid flow analogy of a capacitor discharging.
Cutting to the chase, the formula for voltage as a function of time when a capacitor is
discharging is
( )
t
RC
C
initial
v
t
V
e

=
.
RC is called the time constant for obvious reasons.
At one time constant, the voltage across a capacitance discharging through a resistance is
1
0.368
e

2245
times its initial value.
After about three to five time constants, the
capacitance is almost totally discharged.
Show figure 4.2
Charging a Capacitance from a DC Source through a Resistance
When a dc source is connected in an RC circuit, the total response contains two parts;
forced (or steadystate) and transient.
Figure 4.3
shows a capacitance charging through a resistance.
The switch closes at t=0
connecting the dc source V
S
to the circuit.
At t=0 the voltage across the capacitance
equals zero.
Show figure 4.3 and overlay 4.4.
The formula for voltage across a capacitor that is in series with a source
V
S
and a resistor
R
is as follows:
1
( )
RC
C
S
S
v
t
V
V e

=

As with discharging, the charging rate is 63.2% for each time constant.
Exercise 4.1
Suppose R=5000Ω and C=1μF in 4.1a.
Find the time in which the voltage
across the capacitor reaches 1% of its initial value.
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 Spring '10
 Nawaz
 Steady State, Volt, Inductor, RC circuit, RL circuit, DC source

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