A rectangular copper block has a resistivity \(1.7 \times 10^{-8} \Omega \mathrm{m}\). \(L_1=15 \mathrm{~cm} ; L_2=3 \mathrm{~cm}\). The area of the faces are \(A_1=18 \mathrm{~cm}^2\) and \(A_2=90 \mathrm{~cm}^2\). A current is passed through the length \(L_1\). The resistance of the block is (A) \(1.4 \times 10^{-6} \Omega\) (B) \(1.4 \times 10^{-10} \Omega\) (C) \(5.7 \times 10^{-8} \Omega\) (D) \(5.7 \times 10^{-4} \Omega\) (E) \(7.1 \times 10^{-6} \Omega\)

Understanding how to calculate electrical resistance is crucial for many physics questions, like the one involving our copper block. Resistance, represented by the symbol R, is a measure of how much a material opposes the flow of electric current. It depends on the material's resistivity, the length of the material through which the current flows, and the cross-sectional area perpendicular to that current.

The formula to calculate resistance is:
\( R = \frac{\rho \times L}{A} \)
Here, R is the resistance, \( \rho \) (rho) is the resistivity of the material, L is the length of the material, and A is the cross-sectional area. For instance, in our exercise with the copper block, we used the length L_1 and area A_1 because the current was passed through the length L_1, making A_1 the relevant cross-sectional area. The exercise highlights the practical application of this formula and demonstrates the importance of using the correct measurements for accurate resistance determination.

Resistivity and conductivity are two intrinsic properties that describe how well materials can transport electric charge. Resistivity, represented by the Greek letter \( \rho \), is a measure of a material's ability to resist the flow of electric current. It is dependent on the material and its temperature but does not change with the dimensions of the material.

On the other hand, conductivity, denoted by \( \sigma \), is the inverse of resistivity and measures a material's ability to allow the flow of electric charge. The relationship between resistivity and conductivity is given by: \( \sigma = \frac{1}{\rho} \)
Materials with low resistivity are good conductors, such as copper used in our textbook example, which allows current to flow easily. Conversely, materials with high resistivity are good insulators. Understanding these properties helps in selecting appropriate materials for different electrical applications.

Unit conversion is a fundamental skill in physics, as it allows for the consistent and accurate application of formulas and equations. It's often the first step in solving problems, as seen in the copper block question. Before performing the resistance calculation, we had to convert centimeters to meters and square centimeters to square meters to ensure the correct units were used in the formula.

To convert from a smaller unit to a larger unit, divide by the conversion factor. Conversely, multiply by the conversion factor to go from a larger unit to a smaller unit. For instance, to convert centimeters to meters, you divide the number of centimeters by 100 because there are 100 centimeters in a meter.

Correct unit conversion is crucial to obtaining the right answer. In physics problems, maintaining consistency with SI units, the international system of units, is essential. This system comprises base units like meters for length, kilograms for mass, and seconds for time, all of which are universally recognized and applied.