Câu hỏi 45

u_AB trễ pha hơn i => Z_C > Z_L

Ta có: 

\(\left\{ \matrix{
c{\rm{os}}{\varphi _{AM}} = {R \over {\sqrt {{R^2} + Z_L^2} }} = 0,8 \hfill \cr
c{\rm{os}}{\varphi _{AB}} = {R \over {\sqrt {{R^2} + {{\left( {{Z_L} - {Z_C}} \right)}^2}} }} = 0,6 \hfill \cr} \right. \Rightarrow \left\{ \matrix{
{R^2} = 0,64{R^2} + 0,64Z_L^2 \hfill \cr
{R^2} = 0,36{R^2} + 0,36{\left( {{Z_L} - {Z_C}} \right)^2} \hfill \cr} \right. \Rightarrow \left\{ \matrix{
{Z_L} = 0,75R \hfill \cr
{Z_C} = {{25} \over {12}}R \hfill \cr} \right.\)

\( \Rightarrow {{{Z_L}} \over {{Z_C}}} = {{0,75R} \over {{{25} \over {12}}R}} = 0,36 \Leftrightarrow {\omega ^2}LC = 0,36 \Leftrightarrow {1 \over {LC}} = {{{\omega ^2}} \over {0,36}} \Rightarrow \omega _0^2 = {{{\omega ^2}} \over {0,36}} \Rightarrow {f_0} = {f \over {\sqrt {0,36} }} = {{60} \over {\sqrt {0,36} }} = 100Hz\)