An oscilloscope is a device used to produce different shaped alternating current waveforms. 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 Vcand opens when the potential has dropped to 0.2 V. The emf , 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, ε = 800V, Vc = 4 V, R2=0.001Ω, R1= 0.5 MΩ, and C = 0.02µF. The switch S1 is closed at t = 0.

Engineering

Physics

RC Circuit

Question

An oscilloscope is a device used to produce different shaped alternating current waveforms. 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 Vcand opens when the potential has dropped to 0.2 V. The emf , 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, ε = 800V, V_c = 4 V, R₂=0.001Ω, R₁= 0.5 MΩ, and C = 0.02µF. The switch S₁ is closed at t = 0.

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Linked Question 1

Find the approx. time at which switch S first closes ?

5 × 10^–5 sec

10^–4 sec

0.2 sec

0.01 sec

$Q = CV (1 - e^{- tRC})$
$V_{C} = \frac{Q}{C} = V (1 - e^{tRC})$
$4 = 800 (1 - e^{\frac{- t}{5 \times 10^{5} \times 2 \times 10^{- 8}}}) = 800 (1 - e^{- 100 t})$
$\frac{4}{800} = 1 - e^{- 100 t}$
$\frac{1}{200} \approx 1 - (1 - 100 t) = 100 t$
t = 5 × 10^–5sec.

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Linked Question 2

At what time does switch S first open again after that ?

$\frac{\ln 2}{3} \times 10^{- 8} \sec$

$\frac{\ln 2}{2} \times 10^{- 11} \sec$

$\frac{\ln 20}{5} \times 10^{- 12} \sec$

$\ln 20 \times 10^{- 12} \sec$

Q = CVe^–t/RC
$0.2 = \frac{Q}{C} = 4 e^{\frac{- t}{10^{- 3} \times 2 \times 10^{- 8}}}$
$\frac{1}{20} = e^{- 5 \times 10^{+ 12} t}$
–ln20 = –5 × 10¹² t
$t = \frac{\ln 20}{5 \times 10^{12}} \sec$

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