Ta có:
$I_{1}=\dfrac{U_{V_{1}}}{R_{1}}=\dfrac{2}{R_{1}}$
$I_{V_{1}}=\dfrac{U_{V_{1}}}{R_{v}}=\dfrac{2}{R_{v}}$
$I_{2}=\dfrac{U_{V_{2}}}{R_{2}}=\dfrac{3}{2R_{1}}$
$I_{V_{2}}=\dfrac{U_{V_{2}}}{R_{v}}=\dfrac{3}{R_{v}}$
Ta có: $I_{1}+I_{V_{1}}=I_{2}+I_{V_{2}}$
$⇔\dfrac{2}{R_{1}}+\dfrac{2}{R_{v}}=\dfrac{3}{2R_{1}}+\dfrac{3}{R_{v}}$
$⇔\dfrac{1}{2R_{1}}=\dfrac{1}{R_{v}}$
$⇒R_{v}=2R_{1}$
$R=\dfrac{R_{1}.R_{v}}{R_{1}+R_{v}}+\dfrac{2R_{1}.R_{v}}{2R_{1}+R_{v}}$
$=\dfrac{2.R_{1}²}{3R_{1}}+\dfrac{4R_{1}²}{4R_{1}}$
$=\dfrac{2R_{1}}{3}+R_{1}$
$=\dfrac{5R_{1}}{3}$
$=\dfrac{5R_{v}}{6}$
$⇒\dfrac{R_{v}}{R}=\dfrac{6}{5}$
