1. ## 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

2. Originally Posted by tommoturbo
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?

3. 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