Question

Ajutor, clasa a XI-a.

Answer 1

$\omega=2\pi\nu=100\pi rad/s\\X_L=\omega L=100\pi*\frac{4}{100\pi}=4\Omega\\ Z^2=R^2+X^2_L=3^2+4^2=9+16=25=>Z=\sqrt{25}=5\Omega\\U=ZI=>I=\frac{U}{Z}=\frac{100}{5}=20 A\\ i=I_{max}sin(\omega t+ \varphi)(A)\\I_{max}=I\sqrt2=20\sqrt2A\\tg \varphi=\frac{X_L}{R}=\frac{4}{3}=> \varphi=arctg(\frac{4}{3}) \\ i=I_{max}sin(\omega t+ \varphi)=20\sqrt2sin(100\pi t+arctg(\frac{4}{3})) (A)$

$u_r=U_R_{max}sin(\omega t)(V)\\U_R=R*I=3*20=60 V\\U_R_{max}=U_R\sqrt2=60\sqrt2V\\u_r=U_R_{max}sin(\omega t)=60\sqrt2sin(100\pi t)(V)\\u_L=U_L_{max}sin(\omega t)(V)\\U_L=X_L*I=4*20=80V\\U_L_{max}=U_L\sqrt2=80\sqrt2 V\\u_L=U_L_{max}sin(\omega t)=80\sqrt2sin(100\pi t)(V)$