The molar conductivity of Na1 ions in aqueous solution at 25°C has been determined to be =.01 × 10-2 (V cm)-1 mol-1L. Assume an electric field of 1.0 × 102 V cm-1 is applied to the solution. Calculate the mobility and the drift velocity of Na1 ions.
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- A solid conduetor of eireular eross-setion with a radius of 5 mm has a conductivity that varies with radins. The conductor is 20 m long and there is a potentinl difference of 0.1 V de between its two ends. Within the conductor, II –- 10°p²a, A/m. Find J as a funetion of gA close analogy exists between the flow of energy by heat because of a temperature difference (see Section 19.6) and the flow of electric charge because of a potential difference. In a metal, energy dQ and electrical charge dq are both transported by free electrons. Consequently, a good electri- cal conductor is usually a good thermal conductor as well. Consider a thin conducting slab of thickness dx, area A, and electrical conductivity ơ, with a potential difference dV between opposite faces. (a) Show that the current I = dq/dt is given by the equation on the left: Charge conduction Thermal conduction dq = oA dt dT kA dt dQ AP dx dx In the analogous thermal conduction equation on the right (Eq. 19.17), the rate dQ/dt of energy flow by heat (in SI units of joules per second) is due to a temperature gradient dT/dx in a material of thermal conductivity k. (b) State anal- ogous rules relating the direction of the electric current to the change in potential and relating the direction of…Copper wire has a resistivity p = 1.7 × 10-8 ∙m when at 20°C and it has a temperature coefficient a = 3.9 × 10-³ K-¹. A solid cylinder of copper of length L = 45 cm and diameter D = 1.5 mm has one end held at T₁ = 15°C and the other end is held at T2 = 280°C. The temperature increases linearly between the two ends of the cylinder. T₁ dx L T₂ Consider a thin slice of the copper cylinder of thickness dx that is located a distance x from the left end of the cylinder. Write an equation for the temperature of this slice in terms of the variables x, L, T₁, and T2. Determine the total resistance in milliohms.
- A close analogy exists between the flow of energy by heat because of a temperature difference (see Section 19.6) and the flow of electric charge because of a potential difference. In a metal, energy dQ and electrical charge dq are both transported by free electrons. Consequently, a good electrical conductor is usually a good thermal conductor as well. Consider a thin conducting slab of thickness dx, area A, and electrical conductivity o, with a potential difference dVbetween opposite faces. (a) Show that the current I= dq| dt is given by the equation on the left: Charge conduction Thermal conduction da = GA dt dQ = kA dx dt dx In the analogous thermal conduction equation on the right (Eq. 19.17), the rate dQ/ dt of energy flow by heat (in SI units of joules per second) is due to a temperature gradient dT/ dx in a material of thermal conductivity k. (b) State analogous rules relating the direction of the electric current to the change in potential and relating the direction of energy…Copper wire has a resistivity o = 1.7 x 10-8 22m when at 20°C and it has a temperature coefficient a = 3.9 × 10-3 K-1. A solid cylinder of copper of length L = 85 cm and diameter D = 1.5 mm has one end held at T₁ = 15°C and the other end is held at T2 = 230°C. The temperature increases linearly between the two ends of the cylinder. T₁ dx R= L T₂ Part (a) Consider a thin slice of the copper cylinder of thickness dx that is located a distance x from the left end of the cylinder. Write an equation for the temperature of this slice in terms of the variables x, L, T1, and T2. Part (b) Determine the total resistance in milliohms.Cylindrical-conductors has inner and outer radii of 15 mm and 50 mm, respectively. If V(p = 15 mm) = 0 V and V(p = 50 mm) = 200 V, &r = 10 %3D %3D %D calculate : a. V, E, and D at p = 20 mm b. Ps on each plate.
- Copper wire has a resistivity ρ = 1.7 × 10-8 Ω⋅m when at 20°C and it has a temperature coefficient α = 3.9 × 10-3 K-1. A solid cylinder of copper of length L = 85 cm and diameter D = 3.5 mm has one end held at T1 = 14°C and the other end is held at T2 = 210°C. The temperature increases linearly between the two ends of the cylinder. 1A) Consider a thin slice of the copper cylinder of thickness dx that is located a distance x from the left end of the cylinder. Write an equation for the temperature of this slice in terms of the variables x, L, T1, and T2. The answer to part a is T=( x/L ) T2 + ( 1 - ( x/L ) ) T1 b) Determine the total resistance in milliohms.Copper wire has a resistivity ρ = 1.7 × 10-8 Ω⋅m when at 20°C and it has a temperature coefficient α = 3.9 × 10-3 K-1. A solid cylinder of copper of length L = 85 cm and diameter D = 3.5 mm has one end held at T1 = 14°C and the other end is held at T2 = 210°C. The temperature increases linearly between the two ends of the cylinder. 1a) Consider a thin slice of the copper cylinder of thickness dx that is located a distance x from the left end of the cylinder. Write an equation for the temperature of this slice in terms of the variables x, L, T1, and T2. 2a) Determine the total resistance in milliohms.A block in the shape of a rectangular solid has a cross-sectional area of 4.00 cm^2 across its width, a front-to-rear length of 5.00 cm, and a material conductivity of 10^6 Ω x m^-1. The block’s material contains 5.00x10^22 conduction electrons/m^3. A potential difference of 35.0 V is maintained between its front and rear faces. Find: (a) the resistivity of the block material(b) the resistance of the block(c) the current through the block(d) the magnitude of the current density if it is uniform(e) the drift velocity of the conduction electrons (f) the magnitude of the electric field through the block
- A close analogy exists between the flow of energy by heat because of a temperature difference (see Section 20.7) and the flow of electric charge because of a potential difference. In a metal, energy dQ and electrical charge dq are both transported by free electrons. Consequently, a good electrical conductor is usually a good thermal conductor as well. Consider a thin conducting slab of thickness dx, area A, and electrical conductivity o, with a potential difference dv between opposite faces. (a) Show that the current I = dq/dt is given by the equation on the left: Charge conduction Thermal conduction dq TA dt JdT| kA dt dQ | dx |AP| |dx In the analogous thermal conduction equation on the right (Eq. 20.15), the rate dQ/dt of energy flow by heat (in Sl units of joules per second) is due to a temperature gradient dT/dx in a material of thermal conductivity k. (b) State analogous rules relating the direction of the electric current to the change in potential and relating the direction of…A wire with a radius of 2.22mm is made of a conducting material that has an atomic mass of 72.0 grams/mole and a mass density of 6.17x103 kg/m3. You can assume that each atom of the material has one free electron associated with it. What is the drift speed vd in a 19.3 cm long section of wire that is carrying 664 Amps? Assume 3 significant digits and units of mm/s.Consider electrons flowing in copper. a) Compute the average time between collisions for free electrons in copper. (Hint: The density of free electrons in copper is 8.44 x 1028 electrons / m3). b) Due to quantum mechanical effects, electrons in copper have a speed of about 106 m/s at room temperature. Show that electrons moving at such speeds will travel an average distance of 25 nanometers between collisions.