Lấy cùng một vật liệu làm dây.
\(R_1=\rho\dfrac{l_1}{S_1}\); \(R_2=\rho\dfrac{l_2}{S_2}\)
Ta có : \(\dfrac{R_1}{R_2}=\dfrac{\dfrac{\rho l_1}{S_1}}{\dfrac{\rho l_2}{S_2}}=\dfrac{\rho l_1S_2}{\rho l_2S_1}=\dfrac{l_1S_2}{l_2S_1}=\dfrac{l_1}{l_2}\cdot\dfrac{S_2}{S_1}\left(đpcm\right)\)
Vậy \(\dfrac{R_1}{R_2}=\dfrac{l_1}{l_2}\cdot\dfrac{S_2}{S_1}\)