2 An RC circuit, shown below, has in input voltage u(t) and output voltage v(t). The circuit obeys dv the ODE, RC +v = u, dt 2.1 by solving the ODE, derive an equation which relates the circuit's output voltage to input voltage. (show your working clearly) R u(t) C v(t) 2.2 Using you result for 2.1 calculate the output voltage v(t) if, u(t) = 0. 2.3 Using your result for 2.1, calculate the output voltage v(t) if, u (t) = 1, cos (ot + ø).
2 An RC circuit, shown below, has in input voltage u(t) and output voltage v(t). The circuit obeys dv the ODE, RC +v = u, dt 2.1 by solving the ODE, derive an equation which relates the circuit's output voltage to input voltage. (show your working clearly) R u(t) C v(t) 2.2 Using you result for 2.1 calculate the output voltage v(t) if, u(t) = 0. 2.3 Using your result for 2.1, calculate the output voltage v(t) if, u (t) = 1, cos (ot + ø).
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Transcribed Image Text:An RC circuit, shown below, has in input voltage u(t) and output voltage v(t). The circuit obeys
the ODE, RC +v= u,
dt
2.1 by solving the ODE, derive an equation which relates the circuit's output voltage to input
voltage. (show your working clearly)
R
u(t)
C
v(t)
2.2 Using you result for 2.1 calculate the output voltage v(t) if, u(t) = 0.
2.3 Using your result for 2.1, calculate the output voltage v(t) if, u(t) = 1, cos (@t+ ø).
COS
2.4 Using an exponential Fourier series to express a periodic input voltage, with
fundamental frequency f Hz, as
8.
u(t) = E C,e2rnt
n=-0
(where C, complex numbers), derive the output voltage and show that the above circuit
reduces the amplitude of higher frequency harmonics and is thus a 'low pass' filter.
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