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Thread: Last question, please help? Sum & product formulae.?

  1. #1
    Feb 2009
    NorthWest of England

    Lightbulb Last question, please help? Sum & product formulae.?

    Final question of my assigment, can anyone help me so I can celebrate!!
    I'm struggling on the following question:
    Power in an electric circuit is given by: p = iv
    Calculate the maximum value of power if:
    v = 0.002Sin (100piet)volts
    i = 0.6Sin (100piet + pie/4)amps

    and calculate the first time the power reaches a maximum value??

    I've had a go at calculating maximum power and got the following:

    0.6Sin(100piet + pie/4) x 0.02Sin(100piet)
    = 0.012Sin(100piet) - Sin(100piet + pie/4)
    = 1/2 x 0.012(cos(100piet -(100piet + pie/4))-cos(100piet+(100piet+pie/4))
    = 0.006(cos pie/4 - cos(200piet + pie/4)
    as smallest possible value is -1 for cos(200piet +pie/4)
    : max value of p = 0.006(cos pie/4 +1)
    = 0.0102?
    Does this make any sense?

    For the second part of the question: First time it reaches maximum power, I need some guidance on this one, I'm not sure where to go with this one?

    All help would be greatly appreciated.
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  2. #2
    Junior Member lanzailan's Avatar
    Mar 2009
    as far as i concerned, when multiplying complex number you need to multiply the magnitud and add the phase:

    now you need to transfrom time-domain to phasor-domain

    $\displaystyle v(t)=v_{m}\sin(\omega+\emptyset)\Longleftrightarro w v=v_{m}\angle\emptyset-90^\circ$

    $\displaystyle i(t)=i_{m}\sin(\omega+\emptyset)\Longleftrightarro w i=i_{m}\angle\emptyset-90^\circ$

    $\displaystyle v=0.002\angle-90^\circ,i=0.6\angle-45^\circ$

    $\displaystyle p=vi=0.002\times0.6\angle-45^\circ-90^\circ=1.2\angle-135^\circ mW$
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