Find the fourier series coefficients an bn and a0 -

Question

1- For the following voltage waveform

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

b) Plot v_ac (θ) vs θ n = 1:1:30.

c) Find the THD of v_ac (θ) .

d) Plot the harmonic spectrum of v_ac (θ) for n = 1:1:30. (i.e.: a_n vs. n and b_n vs. n)

2- The voltage waveform is applied to an RL load as shown below. R= 1Ω, L = 1mH ,f = 60 Hz, 0 = 27-t- ft , where t is time in seconds.

Assume ideal passives and steady state operation with initial conditions equal to zero.

For n = 1, 2, 3, 4, 5 and 6, write a MATLAB script that calculates the following

a) P
b) Q
c) S
d) THD
e) pf

3- Repeat question 2, but now for an RC load as shown below, with c = 1μF.

4- An electric resistance space heater rated at 1500 W for an ac voltage source of v(t) = √2 V_rms sin(2Πft), V_rms = 120v, f = 60 Hz has a thermostatically controlled switch. The heater periodically switches on for 5 minutes and off for 7 minutes.

Determine

a) The maximum instantaneous power.

b) The average power over the 12 minutes cycle

c) The electric energy converter to heat in each 12 minutes cycle