AP 3302 Pt. 3
Section 2
CHAPTER 2
Square Waves applied to CR circuits
discharged. The applied voltage V is then zero, Vc is zero and, since there is no current flowing through R, Vr is also zero.
When we switch to the charge position, C cannot change its charge - and hence its voltage - instantaneously, so that the whole of the applied voltage V appears across R. Thus Vr rises immediately to the voltage V of the supply, in this case + 60V; Vc at this instant is zero (Fig 3).
Subsequently Vc begins to rise and will continue to rise exponentially until C is fully charged to +60 V in a time of 5CR seconds. Since at all times Vc+Vr = V, Vr falls exponentially towards zero as Vc rises.
At the instant when C is fully charged to the voltage of the supply (+60V), and Vr is consequently zero, suppose we switch back to the discharge position. This causes the applied voltage V to fall immediately from + 60V to zero. Remembering that C cannot change its charge instantaneously Vc will initially be unaffected by this and remain charged to + 60V. But what of Vr? Since V = Vc+Vr, and the applied voltage V is zero, we have at this instant:
0= Vc + Vr
therefor Vr = -Vc = -60V
Thus at the instant of switching to the discharge position the voltage Vr across R falls immediately to -60V. (The negative sign means that point Pin the circuit of Fig 2 is negative with respect to earth).
