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 \sum ↙\stackrel{3}{k = 1}⁡a_{k}\cos ⁡ (k\omega _{0}t) , where a_{k} \neq 0,\omega_{o} \neq 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?

Correct Answer is : ∑k=13⁡bkcos⁡(kω0t+φk),wherebk≠ak,∀k

\:\sum ↙\stackrel{3}{k = 1}⁡b_{k}\cos ⁡ (k\omega _{0}t + \phi _{k}) ,where\:b_{k} \neq a_{k},\forallk

\:\sum ↙\stackrel{4}{k = 1}⁡b_{k}\cos ⁡ (k\omega _{0}t + \phi _{k}) ,where\:b_{k} \neq 0,\forallk

\sum ↙\stackrel{3}{k = 1}⁡a_{k}\cos ⁡ (k\omega _{0}t + \phi _{k})

\sum ↙\stackrel{3}{k = 1}⁡a_{k} \sin ⁡ (k\omega _{0}t + \phi _{k})

GATE Electronics and Communications (EC) 2016 Shift 1 Solved Paper

Question : 41 of 65

Marks: +1, -0

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

∑ ↙{k = 1}↖{3}⁡a_{k}\cos ⁡ (kω _{0}t) ,

where

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?

$\:∑ ↙{k = 1}↖{3}⁡b_{k}\cos ⁡ (kω _{0}t + φ _{k}) ,where\:b_{k} ≠ a_{k},∀k$
$\:∑ ↙{k = 1}↖{4}⁡b_{k}\cos ⁡ (kω _{0}t + φ _{k}) ,where\:b_{k} ≠ 0,∀k$
$∑ ↙{k = 1}↖{3}⁡a_{k}\cos ⁡ (kω _{0}t + φ _{k})$
$∑ ↙{k = 1}↖{3}⁡a_{k} sin \;⁡ (kω _{0}t + φ _{k})$

Validate

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