Physics, 29.11.2019 08:31, Wildstyle3000
Aresistor is connected in series with an ac source that provides a sinusoidal voltage of v of t is equal to v times cosine of begin quantity omega times t end quantity, where v is the maximum voltage, omega is the angular frequency, and t is the time. the current supplied by this source that flows through this resistor is described with the function i of t is equal to i times cosine of begin quantity omega times t end quantity, where i is the maximum current. what is the average power supplied by this ac source?
Answers: 2
![P=\frac{v_{m}i_{m}}{T}\intop_{0}^{T}(\frac{1+cos(2\omega t)}{2} )dt \\\\P=\frac{v_{m}i_{m}}{T}\intop_{0}^{T}[\frac{1}{2}+\frac{cos(2\omega t)}{2}]dt \\\\P=\frac{v_{m}i_{m}}{T}[\frac{1}{2}(t)\right|_0^T +\frac{sin(2\omega t)}{4\omega} \right|_0^T] \\ \\ P=\frac{v_{m}i_{m}}{2T}[(t)\right|_0^T +\frac{sin(2\omega t)}{2\omega} \right|_0^T] \\ \\ P=\frac{v_{m}i_{m}}{2}](/tpl/images/0395/9473/7d622.png)
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