$$\bbox[yellow, 5px, border: 2px solid red] {\text{R} = \rho \dfrac{l}{\text{A}}}$$
Suatu kawat penghantar panjangnya 2 meter memiliki luas penampang kawat \(5,5 \times 10^{-2}\) mm². Jika hambat jenis kawat \(5,5 \times 10^{-8}\:\Omega \text{ m}\) maka tentukan hambatan kawat penghantar tersebut.
\(\text{R} = \rho \dfrac{l}{\text{A}}\)
\(\text{A} = 5,5 \times 10^{-2}\) mm² = \(5,5 \times 10^{-8}\) m²
\(\text{R} =\cancel{ 5,5 \times 10^{-8}} \cdot \dfrac{2}{\cancel{5,5 \times 10^{-8}}}\)
\(\text{R} = 2 \:\Omega\)
Dua buah kawat penghantar terbuat dari bahan yang sama, panjang kawat pertama empat kali kawat kedua, sedang diameter kawat kedua dua kali diameter kawat pertama. Jika kawat pertama mempunyai hambatan 32 ohm, tentukan hambatan kawat kedua.
\(\rho_1 = \rho_2\) (kedua kawat terbuat dari bahan yang sama)
\(l_1 = 4\cdot l_2\)
\(d_2 = 2\cdot d_1\)
\(\text{R}_1 = 32 \:\Omega\)
\(\text{R}_2 = \text{ ?}\)
\(\dfrac{\text{R}_1}{\text{R}_2} = \dfrac{\cancel{\rho_1} \cdot \dfrac{l_1}{\cancel{\frac{1}{4}\pi} d_1 ^2}}{\cancel{\rho_2} \cdot \dfrac{l_2}{\cancel{\frac{1}{4}\pi} d_2 ^2}}\)
\(\dfrac{\text{R}_1}{\text{R}_2} = \dfrac{\dfrac{l_1}{ d_1 ^2}}{\dfrac{l_2}{d_2 ^2}}\)
\(\dfrac{32}{\text{R}_2} = \dfrac{\dfrac{4\cdot l_2}{ d_1 ^2}}{\dfrac{l_2}{(2\cdot d_1) ^2}}\)
\(\dfrac{32}{\text{R}_2} = \dfrac{\dfrac{4}{1}}{\dfrac{1}{4}}\)
\(\dfrac{32}{\text{R}_2} = 16\)
\(\text{R}_2 = \dfrac{32}{16} = 2 \:\Omega\)
Kawat X dan Y terbuat dari logam sejenis, tetapi diameter kawat X adalah 3 kali diameter kawat Y. Tentukan perbandingan hambatan kawat X terhadap kawat Y jika panjang kawat X adalah 2 kali panjang kawat Y.
\(\rho_x = \rho_y\) (kedua kawat terbuat dari bahan yang sama)
\(l_x = 2\cdot l_y\)
\(d_x = 3\cdot d_y\)
\(\text{R}_1 : \text{R}_2 = \text{ ?}\)
\(\dfrac{\text{R}_x}{\text{R}_y} = \dfrac{\cancel{\rho_x} \cdot \dfrac{l_x}{\cancel{\frac{1}{4}\pi} d_x ^2}}{\cancel{\rho_y} \cdot \dfrac{l_y}{\cancel{\frac{1}{4}\pi} d_y ^2}}\)
\(\dfrac{\text{R}_x}{\text{R}_y} = \dfrac{\dfrac{l_x}{ d_x ^2}}{\dfrac{l_y}{d_y ^2}}\)
\(\dfrac{\text{R}_x}{\text{R}_y} = \dfrac{\dfrac{2\cdot l_y}{ (3\cdot d_y) ^2}}{\dfrac{l_2}{d_2 ^2}}\)
\(\dfrac{\text{R}_x}{\text{R}_y} = \dfrac{\dfrac{2}{9}}{\dfrac{1}{1}}\)
\(\text{R}_x : \text{R}_y = 2 : 9\)
