Introduction to Electric Circuits

8.3 Circuits containing resistance and capacitance 187

accordance with Equation (8.19). The output voltage waveform is then as
shown in Fig. 8.21.

Vo

I

1 I .,.J
0 5~ 1 T+5~ "vt
Figure 8.21

Multiple pulse input

If a train of pulses, for which the pulse width T (>57) is equal to the pulse

separation, is applied to the input terminals then the waveform shown in

Fig. 8.21 will repeat. The capacitor will be fully charged before the end of each

pulse and subsequently fully discharged before the arrival of the next pulse.

This is shown in Fig. 8.22.

Voj

V

5~: T

I

I

2T 3T

Figure 8.22

Pulses for which T < 5z

If the width of the pulse is less than five time constants then the capacitor will
not be fully charged before the pulse is removed (i.e. Vc will be only a fraction
of V). The smaller the pulse width, the smaller the fraction of V reached when
the pulse is removed. However, the time constant CR remains unchanged so
that it takes the same time for the capacitor to become fully discharged after the
pulse is removed, regardless of the pulse width. This is shown in Fig. 8.23, which
is drawn for a pulse width T = 2z.

W o

v

0 2t 7t "--t

if)

Figure 8.23