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If a function f(x) is defined on a infin...

If a function f(x) is defined on a infinite interval `[0, oo]`, then its average value will be `mu= underset(b rarr oo)(lim) (1)/(b) int_(0)^(b) f(x)dx`,
If this limit exists. Find the average power consumption of an alternating current circuit if the current intensity I and voltage u are expressed by the following formulas, respectively:
`I= I_(0) cos (omega t + alpha)`,
`u= mu_(0)cos (omega t + alpha + varphi )`,
where `varphi` is the constant phase shift of the voltage as compared with the current intensity (the parameters `omega and alpha` will not enter into the expression for the average power)

Text Solution

Verified by Experts

The correct Answer is:
`(I_(0)mu_(0))/(2) cos varphi`
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