Đáp án:
$\begin{align}
& {{t}_{nt}}=35phut \\
& {{t}_{//}}=7,14phut \\
\end{align}$
Giải thích các bước giải:
${{t}_{1}}=25p;{{t}_{2}}=10p$
Chỉ dùng một dây:
$\begin{align}
& {{Q}_{1}}={{Q}_{2}}\Leftrightarrow \dfrac{{{U}^{2}}}{{{R}_{1}}}.{{t}_{1}}=\dfrac{{{U}^{2}}}{{{R}_{2}}}.{{t}_{2}} \\
& \frac{25}{{{R}_{1}}}=\frac{10}{{{R}_{2}}} \\
& \Leftrightarrow {{R}_{1}}=2,5{{R}_{2}}(1) \\
\end{align}$
a) khi mắc nói tiếp:
${{R}_{nt}}={{R}_{1}}+{{R}_{2}}=3,5{{R}_{2}}$
thời gian cần:
$\begin{align}
& {{Q}_{2}}={{Q}_{nt}} \\
& \Leftrightarrow \dfrac{{{U}^{2}}}{{{R}_{2}}}.{{t}_{2}}=\dfrac{{{U}^{2}}}{{{R}_{nt}}}.{{t}_{nt}} \\
& \Leftrightarrow \dfrac{10}{{{R}_{2}}}=\dfrac{{{t}_{nt}}}{3,5{{R}_{2}}} \\
& \Rightarrow {{t}_{nt}}=35p \\
\end{align}$
b) Khi mắc song song:
${{R}_{//}}=\dfrac{{{R}_{1}}.{{R}_{2}}}{{{R}_{1}}+{{R}_{2}}}=\dfrac{2,5}{3,5}{{R}_{2}}=\dfrac{5}{7}{{R}_{2}}$
Thời gian:
$\begin{align}
& \dfrac{{{U}^{2}}}{{{R}_{2}}}.{{t}_{2}}=\dfrac{{{U}^{2}}}{{{R}_{//}}}.{{t}_{//}} \\
& \Leftrightarrow \dfrac{10}{{{R}_{2}}}=\dfrac{7}{5}.\dfrac{{{t}_{//}}}{{{R}_{2}}} \\
& \Leftrightarrow {{t}_{//}}=7,14phut \\
\end{align}$
