Sum and Product Formulae: calculate max. value of power in the circuit if...

[Barry1234]

Hi

I am struggling with the following question.

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

\(\displaystyle v = 0.02\sin (100\pi t)\) volts

\(\displaystyle i = 0.6\sin (100\pi t + \frac{\pi}{4} )\) amps

Calculate the first time that the power reaches a maximum value

I have started with the two multiplied together which makes

\(\displaystyle p = V(max) * I(max) \sin (100\pi t) \sin (100\pi t + \frac{\pi}{4} ) \)

Using the trigonometric formula 2.sin A.sin B = Cos(A-B) - Cos(A+B)

\(\displaystyle p = \frac{V(max) I(max)}{2} \cos 100\pi t - \frac{V(max) I(max)}{2} \cos (2 * 100\pi t + \frac{\pi}{4}) \)

Am i going along the right lines??

Thanks for your help

 

[stapel]

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

\(\displaystyle v = 0.02\sin (100\pi t)\) volts

\(\displaystyle i = 0.6\sin (100\pi t + \frac{\pi}{4} )\) amps

Calculate the first time that the power reaches a maximum value

I have started with the two multiplied together which makes

\(\displaystyle p = V(max) * I(max) \sin (100\pi t) \sin (100\pi t + \frac{\pi}{4} ) \)

Maybe I'm not understanding the electrical stuff, but if p = iv, then shouldn't p equal the product of i and v? Where are "V(max)" and "I(max)" coming from? Are you just replacing the "0.02" with "V(max)" and the "0.6" with "I(max)"? If so, by what reasoning? If not, what are you doing?

Have you done calculus at all, so that you could take the derivative to find the max/min time, and then the max/min value?

Thank you!

 

[Barry1234]

Hi stapel

Sorry I changed the I max and v max, I should have kept them as the values below

\(\displaystyle p = \frac{0.02 * 0.6 }{2} \cos 100\pi t - \frac{0.02 * 0.6 }{2} \cos (2 * 100\pi t + \frac{\pi}{4}) \)

If I calculate this then it gives the instantaneous power

I am not sure how to work out the first time the maximum value occurs???

Thanks for your help