What is the Initial Phase Angle and First Maximum Current in an AC Circuit?

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SUMMARY

The initial phase angle of the AC circuit described by the equation i = 15 sin(100πt + 0.6) is 0.6 radians, which converts to approximately 34.38 degrees. To find the first maximum current, the equation 100πτ + 0.6 = π/2 is used, leading to the calculation of time τ as 4.97 x 10^-3 seconds. An algebraic error was identified in the calculation of the first maximum current, indicating the need for careful manipulation of the equations involved.

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  • Understanding of AC circuit equations, specifically i = A sin(ωt + ∅)
  • Knowledge of phase angles in radians and degrees
  • Familiarity with algebraic manipulation of equations
  • Basic concepts of maximum current in AC circuits
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  • Review the derivation of phase angles in AC circuits
  • Learn about the significance of maximum current in sinusoidal functions
  • Study the relationship between angular frequency and time in AC circuits
  • Explore common mistakes in algebraic calculations in physics problems
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This discussion is beneficial for students studying introductory physics, particularly those focusing on AC circuits and phase angles, as well as educators looking for examples of common student errors in algebraic problem-solving.

steveandy2002
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Homework Statement


i = 15 sin(100π.t + 0.6)
a) I need to state the initial phase angel in rads and degrees.
b) I also need to work out current at first maximum value.

Homework Equations


i=A*sin(ωτ+∅)

The Attempt at a Solution



a) ∅=100∏*0+0.6
∅= 0.6 rads. ∴0.6*180/∏=34.37746771°

b) first current max =∏/2 rad's
100∏τ+0.6=∏/2
100τ+0.6=1/2
200τ+1.2=1
t=1/(200+1.2)
t=4.970178926*10^-3
 
Last edited:
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You've made an algebraic mistake in your part b), but yes, you are on the right track. By the way, a thread like this belongs in the "Introductory Physics" forum, not the Calculus forum.
 
Steely Dan said:
You've made an algebraic mistake in your part b), but yes, you are on the right track. By the way, a thread like this belongs in the "Introductory Physics" forum, not the Calculus forum.

where abouts did i go wrong?
 
steveandy2002 said:
100∏τ+0.6=∏/2
100τ+0.6=1/2

:redface:
 

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