We show in Figure the basis of the sweep circuit used in an oscilloscope. S is an electronic switch that closes whenever the potential across its terminals reaches a value V_c and opens when the potential has dropped to 0.2 V. The emf E, much greater than V_c, 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?= 800 V, V_c = 4.2 V, R₂ =

0.001 ?, R₁ = 0.5 M? (0.5 ? 10⁶ ?), and C?= 0.02 ?F.

(a) What is the time constant for charging of the capacitor C?

(b) Show that in the time required to bring the potential across S to the critical potential Vc = 4.2 V, the voltage across the capacitor increases almost linearly with time.

(c) What should be the value of R₁ so that C?charges from 0.2 V to 4.2 V in 0.1 s?

(d) How much time elapses during the discharge of C?through switch S?

(e) At what rate is power dissipated in the resistor R₁ and in the switch resistance?

Transcribed Image Text:

R1 R2