# (A) the Energy Stored in Joules

Department of Electrical Power Engineering

Course Name / Engineering Electromagnetics / Course Code / BEF 22903

Academic Year / 2014/2015 / Semester / II

Tutorial No. 6 / Capacitance

Q1.Two parallel plates spaced 1.0 cm apart in air, each has an area of 1.0 m2. If the p.d. between them is 1000 V, calculate

(a) the energy stored in joules

(b) the force between them.

If the dielectric were mica with r = 7 instead of air, calculate the new values of energy and force.

[Ans. (a) 442 µJ; (b) 0.309 N]

Q2.A parallel-plate capacitor has its plates 0.2 mm apart, with a solid dielectric between having r = 3.3. The capacitor is charged so that surface charge density = 4 x 10-3 µC/cm2. Find the electric flux density and the voltage between the plates.

[Ans. D = 4 x 10-5 C/m2; V = 274 volts]

Q3.A submarine cable is 3000 km long. The inner core is 0.4 cm diameter. The outer core diameter of the gutta-percha (an insulation material) is 1 cm. If the relative permittivity of gutta-percha is 4.05, find the capacitance of the cable.

[Ans. C = 739 µF]

Q4. A capacitor is built up of two coaxial cylinders one metre long. The inner diameter of the outer cylinder is 6 cm and the outer diameter of the inner cylinder is 5 cm. The space between them is filled with insulating material of r = 3.5. Calculate the capacitance and quantity of electricity required to charge it to 22,000 volt.

[Ans. Q = 23.52 µC]

Q5.Derive an expression for the capacitance of a concentric cable and sketch the distribution of the electric field strength in the insulating material.

A 10-kV, 50-c/s concentric cable, 15-km long, takes a charging current of 10 A. The diameter of the core is 0.5 cm and the thickness of the insulation is 0.4 cm. Find the relative permittivity of the insulating material. If a voltage of twice normal value is to be allowed for, what would be the required maximum electric field strength of the material?

Take

Q6.A 100 µµF, concentric-cylinder, compressed-gas capacitor operates at 120 kV and the maximum stress in the dielectric is limited to 6000 kV/m.

Evaluate suitable values for the radius and active length of the inner cylinder if the inside radius of the outer radius is 0.1 m. Establish the formulae used.

Q7.What ratio of outer to inner radius of the dielectric in a concentric cable will result in the minimum electric stress in the dielectric when a given voltage is applied and the outer radius is fixed?

If the inner conductor in such a cable is of 4 cm diameter and the dielectric has a relative permittivity of 3.5, calculate the maximum electric stress in the dielectric when the applied voltage is 300 kV.

Q8.If it is desired that the working voltage of an air-filled coaxial cable having a radius ri = 2 mm for the inner conductor is to remain at 10 kV, what should ro be?

[Answer. 1.571 m]