Maximizing Power in an Electric Circuit: Trigonometric Problem Solution

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SUMMARY

The maximum instantaneous power in an electric circuit is calculated using the formula p = iv, where v = 0.02 sin(100πt) volts and i = 0.6 sin(100πt + π/4) amps. The maximum power occurs when the product of voltage and current is at its peak, which can be determined through trigonometric identities. The first time the power reaches its maximum value can be found by analyzing the phase difference and applying calculus to the power function derived from the given voltage and current equations.

PREREQUISITES
  • Understanding of trigonometric functions and their properties
  • Familiarity with calculus, specifically differentiation
  • Knowledge of electric circuit fundamentals, including voltage and current
  • Ability to apply the product of functions in mathematical analysis
NEXT STEPS
  • Study trigonometric identities and their applications in power calculations
  • Learn about calculus techniques for finding maxima and minima of functions
  • Explore electric circuit analysis, focusing on power calculations
  • Investigate phase relationships in alternating current (AC) circuits
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Electrical engineers, physics students, and anyone interested in optimizing power calculations in electric circuits.

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Can anyone please give me some idea for this problem?
The instantaneous power, p, in an electric circuit is given by p = iv,
where v is the voltage and i is the current.
Calculate the maximum value of power in the circuit if v=0.02 sin(100 pi t)volts and i=0.6 sin(100pi t+ pi/4 ) amp
Calculate the first time that the power reaches a maximum value.[/I]
 
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