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Find the average value in the following ...

Find the average value in the following cases
(i) `i=4+3 cos omegat`
(ii) `5sinomegat + 2sin2omegat + 3sin3omegat`
(iv) `V= cosomegat + 3cos2omegat + 3cos3omegat + 2`

Text Solution

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(i) Average value of current `I_(av) = I_(0) = 4` unit
(ii) Average value of the voltage `V_(av) =0`
(iii) Average value of current `I_(av) =0`
(iv) Average value of voltage `V_(av) = 2`unit
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Find rms value in the following cases (a) I = 5 +3 sin omegat (b) I = a sin omegat + b cos omegat (c ) I =i_(1) sin omegat + i_(2) cos omegat + i_(3) sin 2 omegat .

Which of the following functions represent SHM :- (i) sin 2omegat , (ii) sin omegat + 2cos omegat , (iii) sinomegat + cos 2omegat

Knowledge Check

  • Find the resultant amplitude of the following simple harmonic equations: x_(1)=5 sin omegat x_(2)=5 sin (omgat+53^(@)) x_(3)=-10 cos omegat

    A
    5
    B
    10
    C
    15
    D
    20

  • Funcation x=A sin^(2) omegat+B cos^(2) omegat+ C sin omegat cos omegat Represents SHM.

    A
    For any value of A, B and C (except C = 0).
    B
    If A=B,C=2B and amplitude= `|Bsqrt2|`
    C
    If A=B,C=0
    D
    If A=B,C=2B amplitude=|B|.

  • The rms value of the emf given by E = 8 sin omegat + 6 sin 2omegat .

    A
    `5sqrt2 V`
    B
    `7sqrt2 V`
    C
    `10V`
    D
    `10sqrt2V`

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    Calcualte rms value of current and voltages for the giving cases i) I = 4+3sinomegat ii) V = 5+2 cosomegat (iii) i= 2+3 sinomegat=2cosomegat iv) V =cosomegat + 2cos2omegat

    Which of the following function of time represent (a) periodic and (b) non-periodic motion? Give the period for each case of periodic motion. [w is any positive constant]. (i) sin omegat + cos omegat (ii) sin omegat + sin2 omegat + sin4omegat (iii) e^(-omegat) (iv)log(omegat)

    Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic , and (c) non-periodic motion ? Give period for each case of periodic motion , omega is any positive constant). ltbr. (a) sinomegat-cosomegat) (b) sin^(3)omegat (c) 3cos((pi)/(4)-2omegat) (d) cosomegat+cos3omegat+cos5omegat) (e) exp(-omega^(2)t^(2)) (f) 1+omegat+omega^(2)t^(2)

    Function x = Asin^(2)omegat + Bcos^(2)omegat + C sinomegat represents SHM

    Which of the following equations can form stationary waves? (i) y= A sin (omegat - kx) (ii) y= A cos (omegat - kx) (iii) y= A sin (omegat + kx) (iv) y= A cos (omegat - kx) .

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