Reference no: EM13835429
1- For the following voltage waveform
a) Find the Fourier series coefficients an, bn and a0. Plot the
b) Plot vac (θ) vs θ n = 1:1:30.
c) Find the THD of vac (θ) .
d) Plot the harmonic spectrum of vac (θ) for n = 1:1:30. (i.e.: an vs. n and bn 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 Vrms sin(2Πft), Vrms = 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
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