Question

Circuit RLC serie
R=21 ohmi
L=70 mH
C=82 • 10^-6
R L alcătuiesc o bobina reala
Niu=50 Hz
Uc=310,7 V
Se cere:
Xl, Xc,Z, i mare , Ub,U, f (fi) , tg fi

Answer 1

$X_L=\omega L=2\pi \nu L=2*3,14*70*50*10^{-3} =21,980 \Omega\\X_C=\frac{1}{\omega C}= \frac{1}{2\pi \nu C}=\frac{1}{2*3,14*50*82*10^{-6}}=\frac{10^6}{25748}= 38,83 \Omega\\Z^2=R^2+(X_L-X_C)^2=21^2+(38,83-21,98)^2=441+283,92=724,92=>Z=\sqrt{724,92}=26,92\Omega=>Z=26,92\Omega\\U_C=X_C*I=>I=\frac{U_C}{X_C}=\frac{310,7}{38,83}=8A=>I=8A\\ U^2=U_R^2+(U_L-U_C)^2=I^2[R^2+(X_L-X_C)^2]=I^2Z^2=8^2*26,92^2=46379,92=>U=\sqrt{46379,92}=215,36 V=>U=215,36 V$

$U_b=X_L*I=21,98*8=175,84 V=>U_b=175,84 V\\tg \varphi=\frac{X_C-X_L}{R}=\frac{38,83-21,98}{21}=\frac{16,85}{21}=0,8=> \varphi=arctg(0,8)=>\varphi=38^o 39'$