Consider an AC circuit consisting of a power supply and a resistor. If the current in the circuit at time t is /, then the power delivered to the resistor is /, where R is the resistance. Express the power in terms of cos 2wt

P (t) = Io^2*R*0.5 * (1 - cos (2wt))

Step-by-step explanation:

Given:-

- The given current at time t, with maximum current supplied (Io) is:

I (t) = Io*sin (tw)

Find:-

The power P in terms of cos (2wt)

Solution:-

- The formula for power (P) in an AC circuit is given by the expression:

P (t) = [I (t) ]^2*R

P (t) = [Io*sin (tw) ]^2 * R

P (t) = Io^2*R*sin (tw) ^2

- We will use cos (2w) : Double angle formula as follows,

[sin (wt) ]^2 = 0.5 * (1 - cos (2wt))

- Substituting in our power expression we have:

P (t) = Io^2*R*0.5 * (1 - cos (2wt))