a) b) ww R 45) с I(t) C 00000 Consider a circuit consisting current source connected directly to a capacitor as shown above in (a). Its driving point impedance as seen from the source is Z(s), where the capacitance C = 0.018 F. (a) Suppose the current source varies with time according to I,(t) = 0.001 sin 5.31. i. What is the magnitude of the impedance at that frequency? ii. What is ve(t), the voltage across the capacitor? (please give only the particular solution of the associated differential equation). (b) Suppose the current source is instead constant, given by I,(t)=0.005 Amps. i. What is the magnitude of the impedance at that frequency? ii. What is ve(), the voltage across the capacitor? (please give only the particular solution of the associated differential equation). Note: you may want to solve this using the differential equation directly. (c) Now suppose an inductor with inductance L and a resistor of resistance R are added to the circuit, so that the inductor is in parallel with the capacitor, and both are connected in series with the resistor as shown above in (b). What is the driving point impedance of this new circuit as seen from the current source? For simplicity, please use the symbol C in your answer, rather than its numerical value.
a) b) ww R 45) с I(t) C 00000 Consider a circuit consisting current source connected directly to a capacitor as shown above in (a). Its driving point impedance as seen from the source is Z(s), where the capacitance C = 0.018 F. (a) Suppose the current source varies with time according to I,(t) = 0.001 sin 5.31. i. What is the magnitude of the impedance at that frequency? ii. What is ve(t), the voltage across the capacitor? (please give only the particular solution of the associated differential equation). (b) Suppose the current source is instead constant, given by I,(t)=0.005 Amps. i. What is the magnitude of the impedance at that frequency? ii. What is ve(), the voltage across the capacitor? (please give only the particular solution of the associated differential equation). Note: you may want to solve this using the differential equation directly. (c) Now suppose an inductor with inductance L and a resistor of resistance R are added to the circuit, so that the inductor is in parallel with the capacitor, and both are connected in series with the resistor as shown above in (b). What is the driving point impedance of this new circuit as seen from the current source? For simplicity, please use the symbol C in your answer, rather than its numerical value.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:a)
b)
ww
R
45)
с
I(t)
C
00000
Consider a circuit consisting current source connected directly to a capacitor as shown
above in (a). Its driving point impedance as seen from the source is Z(s), where the capacitance
C = 0.018 F.
(a) Suppose the current source varies with time according to I,(t) = 0.001 sin 5.31.
i. What is the magnitude of the impedance at that frequency?
ii. What is ve(t), the voltage across the capacitor? (please give only the particular solution of
the associated differential equation).
(b) Suppose the current source is instead constant, given by I,(t)=0.005 Amps.
i. What is the magnitude of the impedance at that frequency?
ii. What is ve(), the voltage across the capacitor? (please give only the particular solution of
the associated differential equation). Note: you may want to solve this using the differential
equation directly.
(c) Now suppose an inductor with inductance L and a resistor of resistance R are added to the circuit,
so that the inductor is in parallel with the capacitor, and both are connected in series with the
resistor as shown above in (b). What is the driving point impedance of this new circuit as seen
from the current source? For simplicity, please use the symbol C in your answer, rather than its
numerical value.
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