Un circuit sèrie amb una resistència $R = 10 \ \Omega$ i un condensador $C = 162,48 \ \mu F$ està connectat a una xarxa monofàsica $U = 200 V$ i $f = 50 Hz$
import numpy as np
import matplotlib.pyplot as plt
R = 10
C = 162.48 * 10**(-6)
U = 220
f = 50
w = 2 * np.pi * f
Xc = 0 -1j/(C*w)
Xc
-19.590711852769j
$X_{C} = 19.59_{-90^{\circ}} \ \Omega$
Z = R + Xc
Z
(10-19.590711852769j)
modZ = np.abs(Z)
modZ
21.995362940816044
angZ = np.degrees(np.angle(Z))
angZ
-62.958143957668284
$Z = 22_{-62,96^{\circ}} \ \Omega$
%matplotlib inline
plt.annotate('', xy=(np.real(Z), np.imag(Z)), xytext=(0, 0),
arrowprops=dict(facecolor='blue', shrink=0.05),
)
plt.annotate('', xy=(np.real(Z), 0), xytext=(0, 0),
arrowprops=dict(facecolor='green', shrink=0.05),
)
plt.annotate('', xy=(np.real(Z), np.imag(Z)), xytext=(np.real(Z), 0),
arrowprops=dict(facecolor='red', shrink=0.05),
)
plt.annotate("$Z = 22 \ \Omega$", xy=(1.5, -12))
plt.annotate("$R = 10 \ \Omega$", xy=(6, -3))
plt.annotate("$X_{C} = 19,59 \ \Omega$", xy=(11,-10))
plt.annotate("$62,96^{\circ}$", xy=(2,-2))
plt.xlim(0, 25)
plt.ylim(-25, 0)
plt.axis('off')
plt.show()
fdp = np.cos(angZ)
fdp
0.9920358997298501
$cos(\varphi) = 0,9920$
I = U/Z
I
(4.547371291596367+8.908624066121842j)
modI = np.abs(I)
modI
10.002108198530951
angI = np.degrees(np.angle(I))
angI
62.958143957668284
$I = 10_{62,96^{\circ}} \ A$
%matplotlib inline
plt.annotate('', xy=(10*np.real(I), 10*np.imag(I)), xytext=(0, 0),
arrowprops=dict(facecolor='blue', shrink=0.05),
)
plt.annotate('', xy=(U, 0), xytext=(0, 0),
arrowprops=dict(facecolor='green', shrink=0.05),
)
plt.annotate("$I = 10 \ A$", xy=(50, 100))
plt.annotate("$U = 220 \ V$", xy=(150, 10))
plt.annotate("$62,96^{\circ}$", xy=(30,20))
plt.xlim(0, 250)
plt.ylim(0, 250)
plt.axis('off')
plt.show()
Ur = R * I
Ur
(45.47371291596367+89.08624066121843j)
modUr = np.abs(Ur)
modUr
100.02108198530952
angUr = np.degrees(np.angle(Ur))
angUr
62.958143957668284
$U_{R} = 100_{62,96^{\circ}} \ V$
Uc = Xc * I
Uc
(174.52628708403634-89.08624066121843j)
modUc = np.abs(Uc)
modUc
195.9484196376383
angUc = np.degrees(np.angle(Uc))
angUc
-27.04185604233172
$U_{C} = 196_{-27,04^{\circ}} \ V$
%matplotlib inline
plt.annotate('', xy=(np.real(Ur), np.imag(Ur)), xytext=(0, 0),
arrowprops=dict(facecolor='blue', shrink=0.05),
)
plt.annotate('', xy=(U, 0), xytext=(0, 0),
arrowprops=dict(facecolor='green', shrink=0.05),
)
plt.annotate('', xy=(U, 0), xytext=(np.real(Ur), np.imag(Ur)),
arrowprops=dict(facecolor='red', shrink=0.05),
)
plt.annotate("$U_{R} = 45,47 \ V$", xy=(0, 100))
plt.annotate("$U_{C} = 174,5 \ V$", xy=(125, 75))
plt.annotate("$U = 220 \ V$", xy=(100, 10))
plt.annotate("$62,96^{\circ}$", xy=(30,20))
plt.xlim(0, 250)
plt.ylim(0, 250)
plt.axis('off')
plt.show()
S = U * np.conj(I)
S
(1000.4216841512007-1959.8972945468051j)
modS = np.abs(S)
modS
2200.463803676809
angS = np.degrees(np.angle(S))
angS
-62.958143957668284
$S = 2200_{-62,96^{\circ}} \ VA$
P = np.real(S)
P
1000.4216841512007
$P = 1000 \ W$
Q = np.imag(S)
Q
-1959.8972945468051
$Q = -1960 \ var$
%matplotlib inline
plt.annotate('', xy=(np.real(S), np.imag(S)), xytext=(0, 0),
arrowprops=dict(facecolor='blue', shrink=0.05),
)
plt.annotate('', xy=(np.real(S), 0), xytext=(0, 0),
arrowprops=dict(facecolor='green', shrink=0.05),
)
plt.annotate('', xy=(np.real(S), np.imag(S)), xytext=(np.real(S), 0),
arrowprops=dict(facecolor='red', shrink=0.05),
)
plt.annotate("$S = 2200 \ VA$", xy=(50, -1200))
plt.annotate("$P = 1000 \ W$", xy=(500, -300))
plt.annotate("$Q = -1960 \ var$", xy=(1100,-1000))
plt.annotate("$62,96^{\circ}$", xy=(125,-175))
plt.xlim(0, 2500)
plt.ylim(-2500, 0)
plt.axis('off')
plt.show()