Problem 13 (5 points) (Chap 5.24) (Learning objective: Coaxial capacitor) The capacitance of a particular coaxial cable is 30 pF/m. This cable uses polyethy- lene as the spacer material, having a relative permittivity of 2.25. What is the capacitance of this cable if the spacer material is changed from polyethylene to air?
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- An iron rod with diameter of 1.5-centimeter was formed into an almost perfect circular ring (including the air gap at the joint) having an average centerline radius of 10.0-centimeter. The air gap is 0.25 centimeter in length. A coil of 200 turns was wounded on the ring and a current of 5.0-amperes DC was made to flow using external DC source. Considering magnetic flux fringes on the air gap , the effective cross sectional area of the air gap increased by 5% compared to that of the rod. Relative Magnetic Permeability of Iron = 5500. Consider the average or centerline circumference of the ring as the total magnetic path (rod+airgap). 1. What is the total Reluctance of the ring ( rod + air gap ) (A-turns/Wb) ? 2.What is the magnetic flux generated in the ring? 3. What is the magnetic flux density in the air gapDetermine the mutual inductance between a very long straightwire and a conducting circular loop of radius “b” m set up “d” mapart on the same plane as shown figure.Problem:A coaxial cable of consists of two concentric cylindrical conductors. The region between the conductors is completely filled with polyethylene plastic. The radius of the inner conductor is 0.50 cm, the radius of the outer conductor is 1.75 cm, and the length of the cable is 15 cm. The resistivity of the plastic is 10130- m. Calculate the resistance of the plastic if the electric field is applied across the ends of the conductor. 45.2048 x 1012 ohms O The answer cannot be found on the other choices. O 13.2922 x 1012 ohms 1.6977 x 1015 ohms
- Two long, cylindrical conductors of radii a, and a, are parallel and separated by a distance d, which is large compared with either radius. Show that the capacitance per unit length is given approximately by 1.7 C - TEo In- where a is the geometrical mean of the two radii. Approximately what gauge wire (state diameter in millimeters) would be nec- essary to make a two-wire transmission line with a capacitance of 1.2 x 10-11 F/m if the separation of the wires was 0.5 cm? 1.5 cm? 5.0 cm?The figure is a cross section through three long wires with linear mass density 58.0 g/m. They each carry equal currents in the directions shown. The lower two wires are 4.0 cm apart and are attached to a table. What current I will allow the upper wire to "float" so as to form an equilateral triangle with the lower wires?A coadal cable has a surface charge density of-10 Cim, at the outer conductor and 10 Cim at the inner conductor The inner radius is 2 m, outer Xradius is 6 m and length of this coaxial cable is 100 m. What is the E field inside the inner conductor in between two conductors and outside of the outer conductor (You can leave the expression in terms of permittivity)
- -2nC A neutral Charge below. Sur face enclosing the Canductor (as showon figure) is Conductor with * placed in its cavity as hown a Cavity has a The ' electric flux through the gavesian found to be EE=&E-dA =1 (10) N a) Find the electric charge of t. b) Find the Cmount of of the conductor. () Find the amount of charge on tue outr Susface of the Conductor. Charge on the inner Surface Graussian Surfface 76 F Rain to stopThe figure below is a cross-sectional view of a coaxial cable. The center conductor is surrounded by a rubber layer, an outer conductor, and another rubber layer. In a particular application, the current in the inner conductor is I, = 1.16 A out of the page and the current in the outer conductor is I, = 2.90 A into the page. Assuming the distanced = 1.00 mm, answer the following. d (a) Determine the magnitude and direction of the magnetic field at point a. 2.32e-4 magnitude If you construct an imaginary circle of radius d passing through point a, how much current passes through this circle? UT direction ---Select--- (b) Determine the magnitude and direction of the magnetic field at point b. 1.16e-4 magnitude You can approach this problem by finding the field produced by current I, and the field produced by I, and then adding them vectorially. µT direction ---Select---Does r=e14r=0.788r, which comes in calculation of inductance, play a role in capacitance computations? Yes No
- need problem number 13A ferromagnetic ring has a uniform cross-sectional area of 2000 mm2 and a mean circumference of 1000 mm. A hysteresis loop obtained for the specimen is plotted to scales of 10 mm = 0.1 T and 10 mm = 400A/m and is found to have an area of 104 mm2. Determine the hysteresis loss at a frequency of 80 Hz.A spherical capacitor consists of a conducting sphere of radius a on the inside and a sphere with a radius b of its inner wall as the outer conductor. The gap between them is filled with a dielectric of permeability ɛ. Determine the capacitance. a