$R_{1}=12\Omega$
$R_{2}=4\Omega$
$R_{3}=6\Omega$
$R_{4}=x$
$r=1\Omega$
$E$
2.
$R_{12}=\dfrac{R_{1}.R_{2}}{R_{1}+R_{2}}=\dfrac{12.4}{12+4}=3\Omega$
$R_{123}=R_{12}+R_{3}=3+6=9\Omega$
$⇒R_{N}=\dfrac{R_{123}.R_{4}}{R_{123}+R_{4}}=\dfrac{9x}{9+x}$
$⇒I=\dfrac{E}{R_{N}+r}=\dfrac{(9+x)E}{10x+9}$
$⇒U_{N}=I.R_{N}=\dfrac{(9+x)E}{10x+9}.\dfrac{9x}{9+x}=\dfrac{9x.E}{10x+9}$
$⇒U_{4}=U_{N}$
$⇒P_{4}=\dfrac{U_{4}^{2}}{R_{4}}=\dfrac{81.E^{2}.x}{(10x+9)^{2}}$
$=\dfrac{81.E^{2}}{(10\sqrt{x}+\dfrac{9}{\sqrt{x}})^{2}}$
$⇒P_{4}≤\dfrac{81E^{2}}{4.10.9}=\dfrac{9E^{2}}{40}$
Dấu $=$ xảy ra khi $10\sqrt{x}=\dfrac{9}{\sqrt{x}}$
$⇔x=\dfrac{9}{10}\Omega$
