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Math Help - compond angle formula and adding ac currents?

  1. #1
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    compond angle formula and adding ac currents?

    1. The problem statement, all variables and given/known data

    two alternating currents I1 and I2 flow into a circuit node,the output current I is given by adding I1 and I 2.

    find I and t, when I1 and I2 are as follows

    2. Relevant equations

    I1=5sin(50t +Pi/3)

    I2=6cos50t

    3. The attempt at a solution
    i1=sin(a+b)=sina.sinb+cosa.cosb
    i1=sin50t x cos 60 + sin60 x cos60t x by 1/2 gives
    i1=2.5sin50t + 4.33 x cos50t







    Hi guys help required on above question please not sure where this progresses

    thanks
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  2. #2
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    Quote Originally Posted by tommoturbo View Post
    1. The problem statement, all variables and given/known data

    two alternating currents I1 and I2 flow into a circuit node,the output current I is given by adding I1 and I 2.

    find I and t, when I1 and I2 are as follows

    2. Relevant equations

    I1=5sin(50t +Pi/3)

    I2=6cos50t

    3. The attempt at a solution
    i1=sin(a+b)=sina.sinb+cosa.cosb
    i1=sin50t x cos 60 + sin60 x cos60t x by 1/2 gives
    i1=2.5sin50t + 4.33 x cos50t







    Hi guys help required on above question please not sure where this progresses

    thanks
    I_1 = 5\sin{\left(50t + \frac{\pi}{3}\right)}

     = 5\left[\sin{50t}\cos{\frac{\pi}{3}} + \cos{50t}\sin{\frac{\pi}{3}}\right]

     = 5\left[\frac{1}{2}\sin{50t} + \frac{\sqrt{3}}{2}\cos{50t}\right]

     = \frac{5}{2}\sin{50t} + \frac{5\sqrt{3}}{2}\cos{50t}.


    You also know that I_2 = 6\cos{50t}


    So I = I_1 + I_2

     = \frac{5}{2}\sin{50t} + \frac{5\sqrt{3}}{2}\cos{50t} + 6\cos{50t}

     = \frac{5}{2}\sin{50t} + \frac{12 + 5\sqrt{3}}{2}\cos{50t}.


    I can't see a way to go any further. Were you given any more data? Like some values of I_1 or I_2 for different times?
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  3. #3
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    hello there, thanks for the reply,

    All the info there is what i have im afraid, i thought the i1 value was 5 at the period 50t is this not what it means

    thanks
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