Microscopic View of Current Practice Problems

A pure germanium crystal has a resistivity of 0.60 Ω•m and 2.5 × 10¹³ electrons/cm³ at 20 °C. i) Determine the mean free time for germanium at this temperature. ii) The mean free time for germanium is greater than the mean free time for some conducting materials. Give a reason for the high resistivity of germanium relative to conductors.

In a silicon semiconductor, electrons have an average collision time of 40 ns. An electron takes 3.4 × 10³ minutes to travel 2.0 m within the semiconductor. Find the number of collisions the electron makes with ions over this distance.

Consider two wires A and B, in which the number of electrons flowing per unit of time is the same. The wires are identical in terms of material, but the diameter of wire A is 0.8 cm, and of wire B is 1.6 cm. If in wire A electron drift speed is 3.2 × 10^-4 m/s, find the electron drift speed in wire B.

A 1.8 mm diameter copper wire carries a current of 8.0 A. Determine the magnitude of the electric field required to produce this current in the wire. The conductivity (σ) of copper at room temperature is 5.96 × 10 ⁷ (Ω·m) ^-1.

Consider a copper wire segmented into two different sections, labeled 1 and 2. Both sections, although of different diameters, carry the same constant current of 8.0 A. Determine the drift velocity of the electron in each section. The number density of electrons in copper is 8.5 × 10²⁸ m^-3.

Find the time required for two moles of electrons to pass through a cross-section of a 1.4 mm diameter silver wire, given that the electron drift speed within the wire is 4.2 × 10^-4 m/s. The number density of electrons in silver is 5.86 × 10²⁸ m^-3.

Determine the drift speed of the electron, given that 2.1 × 10¹⁹ electrons pass through a cross-section of a 1.4 mm diameter copper wire in 12s. The number density of electrons in copper is 8.5 × 10²⁸ m^-3.

The electrons in a semiconductor have an average time between collisions of 7.0 ps. Given an electron moves at a drift speed of 3.5 × 10^-3 m/s in the semiconductor, determine the magnitude of the electric field.

In a silver wire, the average time interval between collisions for electrons is 12ps. If the intensity of the electric field is 42 mV/m, determine the speed at which the electron drift.

Calculate the electron drift speed in a 0.75-mm-diameter aluminum wire carrying a small current of 4.5 μA.[Hint: Molar mass of aluminium = 27 × 10^-3 kg/mol, density of aluminium = 2.7 × 10³ kg/m³]

Estimate the current density in a 0.75-mm-diameter aluminum wire carrying a small current of 4.5 μA.

Determine the resistivity ρ of a 4.50-m length of 1.5-mm-diameter tungsten wire that carries a 600-mA current when 18.0 mV is applied across its ends, given that the drift speed is 2.1 x 10⁻⁵ m/s.

Beneath the equator, Ca²⁺ ions with a concentration of 3.0 × 10¹² ions/m³ move east at 2.2 × 10⁶ m/s. Meanwhile, Fe³⁺ ions with a concentration of 6.0 × 10¹¹ ions/m³ move west at 5.5 × 10⁶ m/s. Determine the current density $\overrightarrow{J}$.