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An electrical component has voltage drop $v=V_{m} \sin (\omega t)$, when the current through it is $i=I_{m} \sin (\omega t-\theta)$.

What is the average power dissipated over a half cycle corresponding to $\omega$?

  1. $0$
  2. $V_{m} I_{m} \cos \theta$
  3. $\frac{V_{m} I_{m}}{2} \cos \theta$
  4. $\frac{V_{m} I_{m}}{4} \cos \theta$

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