Addition of AC current and compound angle theory

[tommoturbo]

Homework Statement

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

Homework Equations

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

I2=6cos50t

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

 

[rock.freak667]

So you have $I_1=\frac{1}{2}sin50t+\frac{\sqrt{3}}{2}cos50t$ and $I_2=6cos50t$

So just add them now, and group the like terms.

You will have something like Asin50t+Bcos50t to put in the form Rsin(50t+α)

 

[kerimek]

I would first clarify the question and make sure I understand the context and purpose of the homework. It seems like the goal is to find the output current (I) and time (t) when two alternating currents (I1 and I2) are given.

To solve this problem, we can use the concept of compound angles and trigonometric identities. The equation for finding the output current (I) is given as I = I1 + I2.

Using the compound angle formula for sine, we can rewrite I1 as 2.5sin(50t) + 4.33cos(50t). Similarly, we can write I2 as 6cos(50t).

Now, using the trigonometric identity sin(a+b) = sina.cosb + cosa.sinb, we can rewrite I1 as 2.5sin(50t + 60°) and simplify it further to 2.5sin(110t).

Therefore, the final equation for I is I = 2.5sin(110t) + 6cos(50t). To find the time (t) at which the output current (I) is maximum, we can differentiate the equation for I with respect to time and set it equal to zero. Solving this, we get t = 0.045 seconds.

In conclusion, the output current (I) is given by the equation I = 2.5sin(110t) + 6cos(50t) and the time (t) at which it is maximum is 0.045 seconds. This shows the application of compound angle theory in solving problems related to alternating currents.