Cho mạch RLC. Đặt vào hai đầu đoạn mạch điện áp xo...

B

- Hướng dẫn giải

Ta có:

\(\begin{array}{*{20}{l}}
{P = \frac{{{U^2}.R}}{{{R^2} + {{\left( {{Z_L} - {Z_C}} \right)}^2}}} = \frac{{{U^2}.{R^2}}}{{R.{Z^2}}} = \frac{{{U^2}}}{R}{{\cos }^2}\varphi }\\
{{P_1} = 60\left( {\rm{W}} \right) = \frac{{{U^2}}}{{{R_1}}}{{\cos }^2}{\varphi _1} \Rightarrow \frac{{{{100}^2}}}{{50}}{{\cos }^2}{\varphi _1} = 60 \Rightarrow {{\cos }^2}{\varphi _1} = \frac{3}{{10}}}\\
{{{\cos }^2}{\varphi _1} + {{\cos }^2}{\varphi _2} = \frac{3}{4} \Rightarrow {{\cos }^2}{\varphi _2} = \frac{9}{{20}}}\\
{ \Rightarrow {P_2} = \frac{{{U^2}}}{{{R_2}}}{{\cos }^2}{\varphi _2} = \frac{{{{100}^2}}}{{25}}.\frac{9}{{20}} = 180\left( {\rm{W}} \right)}\\
{ \Rightarrow \frac{{{P_2}}}{{{P_1}}} = \frac{{180}}{{60}} = 3.}
\end{array}\)