A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor(C) elements, connected all in series or all in parallel, is excited with a source of the form$\mathop \sum \limits_{{\rm{k}} = 1}^3 {{\rm{a}}_{\rm{k}}}\cos \left( {{\rm{k}}{{\rm{\omega }}_0}{\rm{t}}} \right),$ where $\rm a_k ≠ 0, ω_o ≠ 0$The source has nonzero impedance. Which one of the following is a possible form of the output measured across a resistor in the network?

Question

A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor(C) elements, connected all in series or all in parallel, is excited with a source of the form$\mathop \sum \limits_{{\rm{k}} = 1}^3 {{\rm{a}}_{\rm{k}}}\cos \left( {{\rm{k}}{{\rm{\omega }}_0}{\rm{t}}} \right),$ where $\rm a_k ≠ 0, ω_o ≠ 0$The source has nonzero impedance. Which one of the following is a possible form of the output measured across a resistor in the network?

TuteeHUB · Accepted Answer

${\rm{\;}}\mathop \sum \limits_{{\rm{k}} = 1}^4 {{\rm{b}}_{\rm{k}}}\cos \left( {{\rm{k}}{{\rm{\omega }}_0}{\rm{t}} + {\phi _{\rm{k}}}} \right),{\rm{where\;}}{{\rm{b}}_{\rm{k}}} \ne 0,\forall {\rm{k}}$

TuteeHUB · Answer

${\rm{\;}}\mathop \sum \limits_{{\rm{k}} = 1}^3 {{\rm{b}}_{\rm{k}}}\cos \left( {{\rm{k}}{{\rm{\omega }}_0}{\rm{t}} + {\phi _{\rm{k}}}} \right),{\rm{where\;}}{{\rm{b}}_{\rm{k}}} \ne {{\rm{a}}_{\rm{k}}},\forall {\rm{k}}$

TuteeHUB · Answer

$\mathop \sum \limits_{{\rm{k}} = 1}^3 {{\rm{a}}_{\rm{k}}}\cos \left( {{\rm{k}}{{\rm{\omega }}_0}{\rm{t}} + {\phi _{\rm{k}}}} \right)$

TuteeHUB · Answer

$\mathop \sum \limits_{{\rm{k}} = 1}^3 {{\rm{a}}_{\rm{k}}}\sin \left( {{\rm{k}}{{\rm{\omega }}_0}{\rm{t}} + {\phi _{\rm{k}}}} \right)$

1.	A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor(C) elements, connected all in series or all in parallel, is excited with a source of the form\(\mathop \sum \limits_{{\rm{k}} = 1}^3 {{\rm{a}}_{\rm{k}}}\cos \left( {{\rm{k}}{{\rm{\omega }}_0}{\rm{t}}} \right),\) where \(\rm a_k ≠ 0, ω_o ≠ 0\)The source has nonzero impedance. Which one of the following is a possible form of the output measured across a resistor in the network?
A.	\({\rm{\;}}\mathop \sum \limits_{{\rm{k}} = 1}^3 {{\rm{b}}_{\rm{k}}}\cos \left( {{\rm{k}}{{\rm{\omega }}_0}{\rm{t}} + {\phi _{\rm{k}}}} \right),{\rm{where\;}}{{\rm{b}}_{\rm{k}}} \ne {{\rm{a}}_{\rm{k}}},\forall {\rm{k}}\)
B.	\({\rm{\;}}\mathop \sum \limits_{{\rm{k}} = 1}^4 {{\rm{b}}_{\rm{k}}}\cos \left( {{\rm{k}}{{\rm{\omega }}_0}{\rm{t}} + {\phi _{\rm{k}}}} \right),{\rm{where\;}}{{\rm{b}}_{\rm{k}}} \ne 0,\forall {\rm{k}}\)
C.	\(\mathop \sum \limits_{{\rm{k}} = 1}^3 {{\rm{a}}_{\rm{k}}}\cos \left( {{\rm{k}}{{\rm{\omega }}_0}{\rm{t}} + {\phi _{\rm{k}}}} \right)\)
D.	\(\mathop \sum \limits_{{\rm{k}} = 1}^3 {{\rm{a}}_{\rm{k}}}\sin \left( {{\rm{k}}{{\rm{\omega }}_0}{\rm{t}} + {\phi _{\rm{k}}}} \right)\)
Answer» B. \({\rm{\;}}\mathop \sum \limits_{{\rm{k}} = 1}^4 {{\rm{b}}_{\rm{k}}}\cos \left( {{\rm{k}}{{\rm{\omega }}_0}{\rm{t}} + {\phi _{\rm{k}}}} \right),{\rm{where\;}}{{\rm{b}}_{\rm{k}}} \ne 0,\forall {\rm{k}}\)

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