`@R_[tđ]=[R_1(R_2+R_3)]/[R_1+R_2+R_3]=20/3(\Omega)`

`=>I=U/[R_[tđ]]=1,5(A)`

`@R_1 //// R_[23]=>U=U_1=U_[23]=10(V)`

  `=>{(I_1=10/10=1(A)),(I_[23]=10/[5+15]=0,5(A)=I_1 =I_2):}`

1,

Ta có: R\(_1\) nt R\(_2\)

\(I_1=\frac{U_1}{R_1}\) , \(I_2=\frac{U_2}{R_2}\)

Mà I\(_1\) = I\(_2\)

\(\Rightarrow\frac{U_1}{R_1}=\frac{U_2}{R_2}\)

\(\Rightarrow\frac{U_1}{U_2}=\frac{R_1}{R_2}\)

* C/m​​​ : \(R_{tđ}=R_1+R_2\)

U = U\(_1\)+U

Ta có: U\(_1\)= I.R\(_1\) , U\(_2\) = I.R\(_2\) , U=I.R\(_{tđ}\)

Mà U =U\(_1\)+U\(_2\)

=>R\(_{tđ}\)=R\(_1\)+R\(_2\)​​​(dpcm)

* C/m \(\frac{Q_1}{Q_2}=\frac{R_1}{R_2}\)

Ta có: \(Q_1=\frac{U^2}{R_1},Q_2=\frac{U^2}{R_2}\)

\(\frac{Q_1}{Q_2}=\frac{\frac{U^2}{R_1}}{\frac{U^2}{R_2}}=\frac{R_1}{R_2}\left(đpcm\right)\)

2, Ta có: \(R_1//R_2\)

\(I_1=\frac{U_1}{R_1}\) , \(I_2=\frac{U_2}{R_2}\)

\(\rightarrow U_1=I_1.R_1\) , \(U_2=I_2.R_2\)

Mà \(U_1=U_2\)

\(\rightarrow I_1R_1=I_2R_2\)

\(\rightarrow\frac{I_1}{I_2}=\frac{R_2}{R_1}\left(đpcm\right)\)

* C/m: \(\frac{1}{R_{tđ}}=\frac{1}{R_1}+\frac{1}{R_2}\)

R\(_{tđ}\)= \(\frac{U}{I}\) = \(\frac{U}{I_1+I_2}\)

\(\rightarrow\frac{1}{R_{tđ}}=\frac{I_1+I_2}{U}\)

\(\Leftrightarrow\frac{I_1}{U}+\frac{I_2}{U}\)

\(\Leftrightarrow\frac{1}{R_1}+\frac{1}{R_2}\)

\(\rightarrow\)\(\frac{1}{R_{tđ}}=\frac{1}{R_1}+\frac{1}{R_2}\)( đpcm )

* C/m \(\frac{Q_1}{Q_2}=\frac{R_2}{R_1}\)

Điện trở tương đương của đoạn mạch

\(R_{tđ}=R_1+\dfrac{R_2R_3}{R_2+R_3}=6+\dfrac{\dfrac{5R_1.5R_1}{2}}{5R_1+\dfrac{5R_1}{2}}=6+\dfrac{5}{3}R_1=16\left(\Omega\right)\)

Cường độ dòng điện qua mạch"

\(I=I_1=I_{23}=\dfrac{U}{R_{tđ}}=\dfrac{12}{16}=0,75\left(A\right)\)

\(\Rightarrow U_{23}=I_{23}R_{23}=0,75.\dfrac{5}{3}R_1=0,75.10=7,5\left(V\right)=U_2=U_3\)

\(\Rightarrow I_2=\dfrac{U_2}{R_2}=\dfrac{7,5}{5R_1}=0,25\left(A\right)\)

\(\Rightarrow I_3=I_{23}-I_2=0,75-0,25=0,5\left(A\right)\)

Thay R2 bằng đèn thì \(I_đ=\dfrac{P}{U}=\dfrac{12}{6}=2\left(Á\right)\)

Rđ=U²/P=6²/12=3(Ω)

\(R_{tđ}=R_1+\dfrac{R_dR_3}{R_đ+R_3}=8,5\left(\Omega\right)\)

\(\Rightarrow I=\dfrac{U}{R_{tđ}}=\dfrac{12}{8,5}=\dfrac{24}{47}\left(A\right)\)

\(\Rightarrow U_{đ3}=IR_{đ3}=\dfrac{60}{47}=U_đ\Rightarrow I_đ=\dfrac{U_đ}{R_đ}=\dfrac{20}{47}\left(A\right)\)

Thấy Id<Idm⇒Đèn sáng yếu hơn bình thường

Điện trở  R 2 :

Đáp số: 1,2A; 20Ω

\(R_{tđ}=\dfrac{U}{I}=\dfrac{84}{6}=14\Omega\)

\(R_{12}=14-10=4\Omega\)

\(R_1//R_2\Rightarrow R_{12}=\dfrac{R_1\cdot R_2}{R_1+R_2}=\dfrac{R_2^2}{2R_2}=\dfrac{R_2}{2}=4\)

\(\Rightarrow\left\{{}\begin{matrix}R_2=8\Omega\\R_1=16\Omega\end{matrix}\right.\)

\(U_1=U_2=U_{12}=U-U_3=84-10\cdot6=24V\)
\(I_1=\dfrac{U_1}{R_1}=\dfrac{24}{16}=1,5A\)

\(I_2=\dfrac{U_2}{R_2}=\dfrac{24}{8}=3\Omega\)

Hiệu điện thế giữa hai đầu  R 3 : U 3  =  I 3 . R 3  = 0,3.10 = 3V.

⇒ U 23 = U 2 = U 3  = 3V (vì  R 2  //  R 3 ).

Cường độ dòng điện qua  R 2 :  I 2 = U 2 / R 2  = 3/15 = 0,2A.

Cường độ dòng điện qua  R 1 : I =  I 1  =  I 2  +  I 3  = 0,3 + 0,2 = 0,5A (vì  R 1  nằm ở nhánh chính,  R 2  và  R 3  nằm ở hai nhánh rẽ)

a, Có : I=I₁=I₂=0,1A (vì R₁ nt R₂)

Có : R_tđ=\(\frac{U}{I}=\frac{12}{0,1}=120\Omega\)

b, Có : R₂=\(\frac{U_2}{I_2}=\frac{6}{0,1}=60\Omega\)

Có : R₁nt R₂ nên :

\(\Rightarrow R_{tđ}=R_1+R_2\)

\(\Rightarrow120=R_1+60\)

\(\Rightarrow R_1=120-60=60\Omega\)

\(R_{23}=\dfrac{R_2.R_3}{R_2+R_3}=\dfrac{10.15}{10+15}=6\left(\Omega\right)\)

\(R_{tđ}=R_1+R_{23}=6+6=12\left(\Omega\right)\)

\(I=I_1=I_{23}=\dfrac{U}{R_{tđ}}=\dfrac{12}{12}=1\left(A\right)\)

\(U_{23}=U_2=U_3=I_{23}.R_{23}=1.6=6\left(V\right)\)

\(\left\{{}\begin{matrix}I_2=\dfrac{U_2}{R_2}=\dfrac{6}{10}=0,6\left(A\right)\\I_3=\dfrac{U_3}{R_3}=\dfrac{6}{15}=0,4\left(A\right)\end{matrix}\right.\)

Chọn A

\(I=I1=I23=\dfrac{U}{R}=\dfrac{12}{6+\left(\dfrac{10\cdot15}{10+15}\right)}=1A\left(R1ntR23\right)\)

\(U23=U2=U3=U-U1=12-\left(1\cdot6\right)=6V\left(R2//R3\right)\)

\(\left\{{}\begin{matrix}I2=U2:R2=6:10=0,6A\\I3=U3:R3=6:15=0,4A\end{matrix}\right.\)

Chọn A