Introduction to Electric Circuits

8.3 Circuits containing resistance and capacitance 191

change but the voltage across the resistor can and it changes immediately to
-10V.
The output voltage waveform can now be drawn as shown in Fig. 8.29.

vo~l

12.5 15 27.5 t(t~S)

-10

Figure 8.29

2 Again the output voltage will immediately jump to 10 V as the first pulse

arrives at the input terminals, for the reason given in part (1). In this case

the pulse width is 5 ~s which is <52 which means that the capacitor will be

only partially charged by the time the trailing edge of any particular pulse

arrives at the input terminals. Also the output voltage will have fallen to a

value >0 and in fact will be given by

Vo = V exp (-t/CR) - 10 exp (-5/2.5) = 1.35 V

At this instant 12 i = 0 so that (Vc + I2R) -- 0 ~ V R --" --V C. But

Vc = (10 - Vo) = (10 - 1.35) V = 8.65 V

SO

v. = Vo = -8.65 V

The voltage across the resistor subsequently rises towards zero. Since the

next pulse in the train arrives after 15 Izs, which is longer than five time

constants, the output voltage becomes zero before it arrives at the input

terminals. The waveform of Vo may now be drawn as shown in Fig. 8.30.

vo(V)

10

1.35

0

-8.65

1

7.5 20 25|

I i 5t

"~ (~s)

Figure 8.30