To find out how many times greater the resistance of a tungsten wire is compared to a silver wire of the same length and cross-sectional area, you can use the formula for resistance, which is given by:
\[ R = \rho \frac{L}{A} \]
where \( R \) is the resistance, \( \rho \) is the resistivity, \( L \) is the length, and \( A \) is the cross-sectional area. For wires of the same length and cross-sectional area, you can compare the resistances directly using their resistivities:
\[ \frac{R_{\text{tungsten}}}{R_{\text{silver}}} = \frac{\rho_{\text{tungsten}}}{\rho_{\text{silver}}} \]
From the table, we have:
- Resistivity of tungsten, \( \rho_{\text{tungsten}} = 5.60 \times 10^{-8} , \Omega \cdot m \)
- Resistivity of silver, \( \rho_{\text{silver}} = 1.59 \times 10^{-8} , \Omega \cdot m \)
Now we can calculate the ratio:
\[ \frac{R_{\text{tungsten}}}{R_{\text{silver}}} = \frac{5.60 \times 10^{-8}}{1.59 \times 10^{-8}} \]
Calculating this gives:
\[ \frac{R_{\text{tungsten}}}{R_{\text{silver}}} \approx \frac{5.60}{1.59} \approx 3.52 \]
Thus, the resistance of a tungsten wire is approximately 3.52 times greater than the resistance of a silver wire of the same length and cross-sectional area.
The correct response is:
3.52
1 answer