Addition of AC current and compound angle theory

Click For Summary
SUMMARY

The discussion focuses on the addition of two alternating currents, I1 and I2, represented by the equations I1=5sin(50t + π/3) and I2=6cos(50t). The output current I is derived by combining these two currents, leading to the expression I = A sin(50t) + B cos(50t). Participants emphasize the importance of grouping like terms and converting the result into the form R sin(50t + α) for further analysis.

PREREQUISITES
  • Understanding of alternating current (AC) theory
  • Familiarity with trigonometric identities
  • Knowledge of phasor representation in electrical circuits
  • Basic calculus for analyzing sinusoidal functions
NEXT STEPS
  • Study the conversion of sinusoidal functions into phasor form
  • Learn about the superposition principle in AC circuits
  • Explore the use of complex numbers in AC analysis
  • Investigate the implications of phase angles in circuit behavior
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing AC circuits will benefit from this discussion.

tommoturbo
Messages
33
Reaction score
0

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
 
Physics news on Phys.org
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)
 

Similar threads

How Do You Calculate the Amplitude of Combined Alternating Currents?
  • · Replies 34 ·
2
Replies
34
Views
4K
Sinusoidal current phase angle question
  • · Replies 1 ·
Replies
1
Views
3K
RMS voltage, phase angle, AC circuits
  • · Replies 1 ·
Replies
1
Views
9K