The figure below shows the basis of the sweep circuit used in an oscilloscope. Switch S is an electronic switch that closes whenever the potential across the switch increases to a value Vc and opens when the potential across the switch decreases to 0.200 V. The emf e m f, which is much greater than Vc, charges the capacitor C through a resistor R1. The resistor R2 represents the small but finite resistance of the electronic switch. In a typical circuit, e m f = 750 V, Vc = 4.60 V, R2 = 1.10 M?, R1 = 0.480 M?, and C = 21.0 nF.
(a) What is the time constant for charging of the capacitor C.
__________ ms
(b) Show that as the potential across switch S increases from 0.190 V to 4.60 V, the potential across the capacitor increases almost linearly with time. Hint: Use the approximation ex ? 1 + x, for |x| << 1. (This approximation of ex can be derived using the differential approximation.)
(c) What should the value of R1 be changed to so that the capacitor charges from 0.190 V to 4.60 V in 0.110 s?
__________ G?
(d) How much time elapses during the discharge of the capacitor when switch S closes?
__________ ps
(e) At what average rate is energy delivered to the resistor R1 during charging and to the switch resistance R2 during discharge?
P1 = __________nW
P2 = __________ kW