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- 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 , with a potential difference dV between opposite faces. (a) Show that the current I = dq/dt is given by the equation on the left: ChargeconductionThermalconductiondqdt=A|dVdx|dQdt=kA|dTdx| 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 flow to the change in temperature.4) Gold wire Al = 10 m long cylindrical wire made of gold (resis- tivity pAu = 2.44 × 10¬8 Nm at To = 20° C, temperature coefficient aAu = 3.4 x 10-3 (°C)¯) has a resistance of R = 12. a: What is the radius r of the wire? b: If the wire is twice as long, the radius is ... 1. twice as big O 2. 2 larger O 3. a fourth O c: What is the resistance of the wire at T 1000° C? %3DWhen a voltage is applied to a conductor, the current that flows is limited by resistance. Which of these factors affects the resistance? Check all that apply. The size of the current, that is, the more current the more resistance there is. The collision of electrons with atoms and the resulting scattering from their direction of movement. The properties of the conducting material, perhaps given as an empirical resistivity. The length of the conductor. The limited cross-sectional area of the conductor.
- Which of the following statements is/are ALWAYS TRUE for the resistivity and conductivity of a material? I. The resistivity of a material is temperature-dependent. II. The conductivity of a material is temperature-dependent. III. As the resistivity of a material increases. its conductivity decreases.13. A very long straight, cylindrical wire lying along the x axis has a diameter of 0.250 mm and is initially at 20.0°C. It is made of a material described by Ohm's law with a resistivity of po = 3.30 x 10-8 Q. m and a temperature coefficient of resistivity of a = 0.00025 °C-1. Using a voltmeter, we measure a voltage of 8.00 V at a point that is 0.750 m to the right of a point that is measured to have zero voltage (see figure below). · Ax = 0.750 m - V= 0 V = 8.00 V a) What is the resistance per unit length of the wire? b) What are the magnitude and direction of the electric field in the section of the wire between the dashed lines? c) What are the magnitude and direction of the current in the wire between the dashed lines? d) What is the rate at which energy is dissipated in the section of the wire between the dashed lines? e) Now assume that the current found in part (c) flows through the entire wire. What is the magnitude and direction of the magnetic field generated by the wire at…1. Gold wire (resistivity p=2.44 x 108 Qm) with a diameter of 2.0 mm is being unwound and a certain length is selected. (a) What should be the length if we want the selected wire to have a resistance of .10 Q? (b) If I put the wire across a potential difference of 30 V, how much energy is dissipated as heat in an hour?
- 11. Consider a wire with conduction electron density 5.9 x 1028 1. If the diameter of the wire is 1.5 mm, and the drift speed of the electrons in the wire is 3.7 × 10-3", how long does it take for 1 mole of electrons to move through a cross section of the m3 S wire? (include units) (Hint: The cross section of the wire is a cir- cle)5. How many free electrons are there in a rectangular block of a conductor whose dimension is 8 m by 4 m by 3 m? The electrons of this conductor have a drift velocity of 4 m/s when a 9.6 A of current is applied thru a cross-sectional area of 0.005 m?. Use electronic charge of 1.6 x 10-19 coulomb per electron. Express your answer in scientific notation whose unit is electrons per cubic meter.1. Calculate the number of free electrons in a copper conductor having a diameter of 0.064in and a length of 1000ft. 2. A current of 5A exist in a 10ohms resistance for 4 minutes. A) How many coulombs B) How many electrons pass through any section of the resistor in this time? Charge of e= 1.6x10^-19. 3. The electric charge that moves through a conductor varies in accordance with the equation q=800t, where q and t are given in coulombs and milliseconds, respectively. Calculate the current in Ampere. 4. Determine the total charge entering a terminal between t=2s, if the current passing the terminal is I= (3t^2-t)A
- 1. Solve the following resistance problems: a. A 4.2 cm long copper wire has a cross-sectional area of 3.7 mm2. Determine the resistance of that wire. Check the resistivity of copper int the table given in the textbook. (1.72 x 10) b. Consider a 1.6 cm long silver wire. What is the cross-sectional area of the wire for it to have a resistance of 2.2 x 10-2 Q.The table given below shows the resistivity of three Material X, Y and Z? Samples X Y Z Resistivity 3 X 10-9 11.1 X 0-6 18X10-17 a. Arrange the samples in increasing order of conductivityb. Which of these is best conductor?c. Which are these is best insulator?1. An aluminium wire with a square cross-section 4 mm on a side is carrying a current of 4.5 amps. Aluminium has a resistivity of 2.69 x 10-6 ohm-cm and an atomic volume of 10 cc/mol. Assuming aluminium has three free electrons per atom, calculate the (a) Hall coefficient, (b) electric field, (c) power dissipated (heat generated) per cm length, and (d) the Hall voltage across the wire in a transverse magnetic field of 1 tesla. [5]
