BEF 22903 T8 Electrical Conduction in Matter

UNIVERSITI TUN HUSSEIN ONN MALAYSIA Department of Electrical Power Engineering Course Name Engineering Electromagnetics Course Code BEF 22903 Academic Year 2014/2015 Semester II Tutorial No. 8 Electrical Conduction in Matter

Q1. Calculate the mobility and relaxation time of the electrons in a silver conductor material. The electrons per unit volume are 5.8 x 1028 in number. The resistivity of the material is 1.54 x 10-8 ohm.m at room temperature. Also calculate the electron drift velocity if the field intensity in the material is 1 volt/cm. -4 -3 2 [Ans.  = 4 x 10 s; µe = 7 x 10 m /v.s;  = 0.7 m/s]

Q2. A copper conductor of cross-section area 2.1 x 10-6 m2 has a current of 20 amperes. Find the mean velocity of electron flow in the conductor. Assume that there are 8.5 x 1028 electrons per cubic metre of copper material. Take the electronic charge e = 1.609 x 10-19 coulombs. [Ans.  = 0.7 x 10-3 m/s.]

Q3. A copper conductor of resistance 100 ohms at 40 °C is heated up to 100 °C. The

temperature coefficient of resistance at zero degree centigrade, 0 = 0.00427 per degree. Calculate the resistance when the conductor is at 100 °C.

[Ans. R100°C = 121.8 ]

Q4. A specimen of conductor material in the form of a wire has a cross-section are of 0.1 mm2 and length 1 metre. If the resistance measured of this specimen is 0.172, calculate the resistivity of the material. [Ans.  = 1.72 x 10-8 .m/cm2]

Q5. A lead ( = 5 x 106 mhos/m) bar of square cross section has a hole bored along its lengh of 4 m so that its cross section becomes that of the figure below. Find the resistance between the square ends.

1 cm 3 cm

Figure Q5. Q6. A rod whose cross section is an equilateral triangle of side 4 cm is 3 metre long. Calculate the resistance bewteen the ends of the rod if it is made of hard rubber ( = 10-15 mhos/m).

Q7. A composite conductor 10 m long consists of an inner core of steel of radius 1.5 cm and an outer sheath of copper whose thickness is 0.5 cm. (a) Determine the resistance of the conductor. (b) If the total current in the conductor is 60 A, what current flows in each metal? (c) Find the resistance of a solid copper conductor of the same length and cross- sectional area as the sheath. Take the resistivities of the copper and steel as 1.77 x 10-8 and 11.8 x 10-8 .m respectively.

Q8. An aluminium bus bar in the shape of a rectangular parallelepiped has a conductivity of σ = 3.5 x 107 mhos/m and a length of 10 m. The two end surfaces of the busbar are each 1 by 2 in. and are designated a and b. A voltage vab = 0.022 volt is applied to the busbar. Evaluate J and E when k is directed from a to b.

Q9. Find the insulation resistance per metre of a single-core cable from the following data”- Core radius = 1.3 cm Outer diameter of cable = 8 cm Specific resistance of insulation material,  = 8 x 1014 ohm.metre. [Ans. R = 1.43 x 1014 ]

Q10. A hollow cylinder of length 2 m has its cross section as shown in the figure below. If the cylinder is made of carbon ( = 105 mhos/m), determine the resistance between the ends of the cylinder. Take a = 3 cm, b = 5 cm.

Figure Q10.

Q11. A 1.0-m-long carbon pipe of inner diameter 3.0 cm and outer diameter 5.0 cm is cut in half lengthwise. Determine the resistance between the inner surface and the outer surface of one of the half sections of pipe. Q12. A conductor specimen is in the form of a 45° C sector of outer thickness d and outer and inner radii of r2 and r1. Calculate the resistance R between the curved edges AA’ and BB’ for a resistivity of  ohm.m.

A’ B’

Figure Q12.

Q13. A 1.0-cm-diameter conductor is sheathed with a 0.50-cm thickness of Teflon and then a 2.0-cm (inner) diameter outer conductor. (a) Use Laplace’s equation to find an expression for the potential as a function of  in the dielectric. (b) Find E as a function of . (c) What is the maximum potential difference that can be applied across this cable without breaking down the dielectric?

Q14. Use Laplace’s equation to find V and E as a function of  within the dielectric of a coaxial cable of inner conductor radius a and outer conductor radius b.

ln   lnb V [Ans: (i) V ()  V ; (ii) E  ab rˆ ] ab ln a  ln b  ln b / a