Question

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Cho R1nt R2 Chứng minh rằng U1/U2=R1/R2; Rtđ=R1 + R2; Q1/Q2=R1/R2
Cho R1// R2 Chứng minh rằng I1/I2=R2/R1; 1/Rtđ= 1/R1 + 1/R2; Q1/Q2=R2/R1

Answer 1

[Nguyễn Thị Thanh Nhàn]

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

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

Answer 2

[Nguyễn Thị Thanh Nhàn]

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 \(\frac{Q_1}{Q_2}=\frac{R_2}{R_1}\)