jangyasinniTeacher
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To find the angle by which the third harmonic current will lead or lag the third harmonic output voltage in a single-phase full-bridge inverter with an RLC load, we need to determine the impedance of the RLC circuit at the third harmonic frequency.
1. Determine the Third Harmonic Frequency:
The fundamental frequency is 50 Hz, so the third harmonic frequency, ( f_h ), is:
[
f_h = 3 times 50 , text{Hz} = 150 , text{Hz}
]
2. Calculate the Reactance:
– Inductive reactance ( X_L ):
[
X_L = 2 pi f_h L = 2 pi times 150 times 35 times 10^{-3} approx 31.42 , Omega
]
– Capacitive reactance ( X_C ):
[
X_C = frac{1}{2 pi f_h C} = frac{1}{2 pi times 150 times 155 times 10^{-6}} approx 10.25 , Omega
]
3. Calculate the Total Impedance ( Z ):
The total impedance ( Z ) of the RLC circuit is given by:
[
Z = R + j(X_L – X_C) = 4
d
Explanation:
X
L = 2 x 3.14 x 50 x 0.035 = 10.99 Ω
X
C = 1/(2 x 3.14 x 50 x 155 x 10
-6
) = 20.54 Ω
For the third harmonic component
X
L
(3rd harmonic) = 10.99 x 3 = 33 Ω (approx.)
X
C
(3rd harmonic) = 20.54/3 = 6.846 Ω
R = 4 Ω
P = tan
-1
(X
L – X
C
)/R = 81.3°