Why Does My Capacitance Power Calculation Not Match the Given Answer?

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SUMMARY

The discussion centers on the calculation of current, power, and energy for a capacitor with a capacitance of 0.01 Farads and a voltage function of v(t) = 100*cos(2π60t). The user correctly calculated the current as i(t) = -120π*sin(2π60t) Amperes but found a discrepancy when calculating power, which did not match the expected answer of -18,850sin(2π120t) Watts. The solution involves applying a trigonometric identity for Sin(2X) to reconcile the calculations.

PREREQUISITES
  • Understanding of capacitor behavior in AC circuits
  • Familiarity with trigonometric identities, specifically Sin(2X)
  • Knowledge of calculus for integration of power to find energy
  • Basic electrical engineering concepts, including current and power equations
NEXT STEPS
  • Study the application of trigonometric identities in AC circuit analysis
  • Learn about the relationship between current and voltage in capacitive circuits
  • Explore integration techniques for calculating energy stored in capacitors
  • Review the derivation of power equations in reactive components
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Students in electrical engineering, particularly those studying circuit analysis and power calculations involving capacitors, as well as educators looking for examples of common calculation errors in AC circuits.

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Homework Statement



The voltage across a capacitor with a value of 0.01 Farads is v(t) 100*cos(2pi60t). Find i(t),p(t),and w(t).


Homework Equations



i(t)=Cv'(t) [current]
p(t)=i(t)v(t) [power]
w= integral of p(t) [Energy stored over time]

The Attempt at a Solution



I was able to correctly determine the current of capacitance, -120*pi*sin(2pi60t) Amperes. However, this multiplied by the voltage, does NOT equal the given answer of -18,850sin(2pi120t) Watts.

Could someone please clear this up for me? I would've used proper symbols, but the test is quite shortly, no time to mess with that ... :/

Thanks!
 
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Try using a trig identity for Sin(2X).
 

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