Question

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

Answer 1

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

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) )