Find the average of the voltage and current and find the

Question

1 - Assume the following is given across a resistive load.

v(t) = Acos(θ)
i(t)=Bcos(θ)

a) Find the average of the voltage and current for 0 ≤ θ ≤ 2Π.

b) Find the average power and show that (v(t))(i(t)) # P in general.

c) Find the rms component of the voltage. How does V_rms relate to P?

d) An inductor is added. Now the load is an RL load. Find the average power across the load.

2- For the following waveform

a) Find the Fourier series coefficients a_n, b_n and a₀.

b) Write a MATLAB function that accepts a_n, b_n, a₀, θ, and n (number of harmonics) and outputs the function. The function form should be similar to function fth = fourier_series(a0,an,bn,n,theta)

c) Use the function you wrote to plot f (θ) vs θ for n=1, n=1:1:5 and n=1:2:5 and n=1:1:30. Which plot gives the closest resemblance to the original waveform shown above.

d) Plot the harmonic spectrum of f (θ) . (i.e.: a_n vs n and b_n vs. n )

3- Prove that the average current across a capacitor is equal to zero.