Some properties of a small piece of germanium wire are shown below.Length,  Cross-section,  Resistivity,     What is its resistance,  ?

To determine the resistance of the germanium wire, we can use the formula for resistance in a conductor:

Step 1: Break Down the Problem

1. Identify the relevant properties of the wire:
   • Length (L)
   • Cross-section area (A)
   • Resistivity (ρ)

Step 2: Relevant Concepts

1. The formula to calculate the resistance (R) of a wire: $R = \frac{\rho L}{A}$ Where:
   • $R$ = resistance in ohms (Ω)
   • $\rho$ = resistivity in ohm-meters (Ω·m)
   • $L$ = length of the wire in meters (m)
   • $A$ = cross-sectional area in square meters (m²)

Step 3: Analysis and Detail

1. Substitute the known values into the formula to calculate the resistance.

   • For example, if:
     • Length $L = 2 \, \text{m}$
     • Cross-section $A = 1 \times 10^{-6} \, \text{m}^2$ (which is 1 mm²)
     • Resistivity $ρ = 0.45 \, \text{Ω·m}$

   Then, $R = \frac{(0.45 \, \text{Ω·m}) \times (2 \, \text{m})}{1 \times 10^{-6} \, \text{m}^2}$

Step 4: Verify and Summarize

1. Perform the calculation: $R = \frac{0.9 \, \text{Ω·m}}{1 \times 10^{-6} \, \text{m}^2} = 900000 \, \Omega = 900 \, kΩ$

Final Answer

The resistance of the germanium wire is $R = 900 \, kΩ$.