CHÚC BẠN HỌC TỐT !!!!!!!!!!!!!
Đáp án:
`U_{V_3} ~~ 1,662 (V)`
Giải thích các bước giải:
Mỗi vôn kế có điện trở là $R_V (\Omega)$.
$U_{AC} + U_{BD} = U_{V_1} - U_{V_2}$
$= 22 - 6 = 16 (V)$
Ta có:
`R_{EF} = {3R_VR}/{3R + R_V}`
`{U_{AC} + U_{BD}}/U_{CD} = {2R}/R_{CD} = 16/6`
`<=> R_{CD} = 3/4 R`
`<=> {(2R + {3R_VR}/{3R + R_V}).R_V}/{R_V + 2R + {3R_VR}/{3R + R_V}} = 3/4 R`
`<=> 4R_V .(2R + {3R_VR}/{3R + R_V}) = 3R.(R_V + 2R + {3R_VR}/{3R + R_V}`
`<=> 4R_V .[2R(3R + R_V) + 3R_VR] = 3R.[(R_V + 2R)(3R + R_V) + 3R_VR]`
`<=> 4R_V .(6R^2 + 5R_VR) = 3R .(R_V^2 + 8R_VR + 6R^2)`
`<=> 4R_V .(6R + 5R_V) = 3.(R_V^2 + 8R_VR + 6R^2)`
`<=> 24R_VR + 20R_V^2 = 3R_V^2 + 24R_VR + 18R^2`
`<=> 17R_V^2 = 18R^2`
`<=> R_V^2 = 18/17 R^2`
`\to R_V = \sqrt{18/17} R`
`\to R_{EF} = {3R_VR}/{3R + R_V} = {3. \sqrt{18/17} R.R}/{3R + \sqrt{18/17} R}`
`= {\sqrt{18/17} R}/{1 + \sqrt{2/17}}`
`= {3\sqrt{2}R}/{\sqrt{17} + \sqrt{2}}`
Ta có:
`{U_{V_2} - U_{V_3}}/{2R} = U_{V_3}/{R_{EF}} = {U_{V_2} - U_{V_3} + U_{V_3}}/{2R + R_{EF}`
`<=> U_{V_3} = {U_{V_2}R_{EF}}/{2R + R_{EF}}`
`= {6. {3\sqrt{2}R}/{\sqrt{17} + \sqrt{2}}}/{2R + {3\sqrt{2}R}/{\sqrt{17} + \sqrt{2}}}`
`~~ 1,662 (V)`
