Let's address each part of the content in the image:

Questions and Explanations

1. Effect of Increasing Length on Resistance
   Increasing the length of a conductor increases its resistance. This is because electrons have to travel a greater distance through the material, encountering more collisions with atoms.

2. Effect of Increasing Cross-Sectional Area on Resistance
   Increasing the cross-sectional area decreases the resistance. A larger area allows more paths for electrons to flow, reducing the overall resistance.

3. Expression for Resistivity
   Starting with the formula for resistance:
   $R = \frac{\rho \cdot l}{A}$
   Rearranging for resistivity ($\rho$):
   $\rho = \frac{R \cdot A}{l}$

4. Units for Resistivity
   Using $R = \frac{\rho \cdot l}{A}$:

   • Resistance ($R$) is measured in ohms ($\Omega$).
   • Length ($l$) is in meters ($m$).
   • Cross-sectional area ($A$) is in square meters ($m^2$).
     Rearranging units for $\rho$:
     $\rho = R \cdot \frac{A}{l} \Rightarrow \rho \, [\text{unit}] = \Omega \cdot m$
     Thus, the unit of resistivity is $\Omega \cdot m$.

5. Resistivity of Various Materials
   Let me search for the resistivity values of graphite, tungsten, glass, and gold.()ivity quantifies how strongly a material opposes the flow of electric current. Materials with lower resistivity are better conductors, while those with higher resistivity resistivity values for graphite, tungsten, glass, and gold:

Note: The resistivity of graphite varies depending on its orientation relative to the basal plane. citeturn0search0

These values indicate that gold has the lowest resistivity among the listed materials, making it an excellent conductor. Tungsten also exhibits low resistivity, though higher than gold, and is commonly used in applications requiring high melting points and good conductivity Graphite's resistivity varies with its structural orientation, offering moderate conductivity. Glass, with its high resistivity, serves as an effective insulator. you have further questions or need more details, feel free to ask.

Related Questions:

1. How does temperature affect the resistivity of these materials?
2. What are the practical applications of tungsten's electrical properties?
3. How does the structure of graphite influence its electrical conductivity?
4. Why is gold preferred over copper in certain electrical applications despite its higher cost?
5. What factors contribute to the high resistivity of glass?

**Tip:**When designing electrical circuits, selecting materials with appropriate resistivity is crucial to ensure efficiency and safety.