Question

Given a series RLC circuit with V = 5V, R = 200 kΩ, C = 10µF. Sampling frequency of the circuit is 10 Hz. The samples x (n), where n=0,1,2,…., is ___________

(a) 5(1-e^-0.05n)

(b) 5e^-0.05n

(c) 5(1-e^-5n)

(d) 5e^-5n

The question was posed to me during an interview.

My doubt is from Discrete Fourier Transform in division Fourier Transform of Signals and Systems

Answer 1

Right answer is (b) 5e^-0.05n

Easy explanation: The charging current in circuit I (t) = I (0^+) e^-t/RC

Since the capacitor acts as short circuit, I (0^+) = \(\frac{V}{R}\)

∴ I (t) = \(\frac{V}{R}\)  e^-t/RC

Voltage across resistor = R I (t)

= V e^-t/RC = 5 e^-t/RC

= 5 \(e{\frac{-t}{200 × 10 × 10^{-6} × 10^3}}\)  = 5 e^-t/2

Given that, the Sampling frequency of the circuit is 10 Hz

∴ x (n) = 5e^-n/2 X 10 = 5e^-0.05n.