Reference no: EM132328155

Assignment Task - Answer the Following Questions

Question :1 Suppose that the voltage waveform shown below is applied to a 10μF capacitance. Find and plot the current, the power delivered, and the energy stored for time between 0 and 5s.

Question :2 The voltage through a 5H inductance is shown below. The initial current in the 9nductor is OA. Plot the current, power, and stored energy versus time for t between 0 and 5s.

Question :3 A parallel-plate capacitor has two plates each of area 5 x10^-3 m² separated by a 2 mm thick sheet of mica of relative permittivity 5. The capacitor is charged to a potential difference of 500 V. Determine:

(a) the electric field strength in the mica;

(b) the flux density in the mica;

(c) the energy stored per cubic metre in the mica.

Question :4 A voltage of 6 kV is maintained between the plates of o parallel plate capacitor. The area of each plate is to 10⁴ mm² and they are separated by 6 mm. Calculate the field strength and flux density between the plates, and the capacitance:

(a) if the separating medium is air.

(b) if an epoxy resin dielectric of relative pemnittivity 5 and thickness 6 mm is placed between the plates.

(c) if the dielectric thickness is only 5 mm (calculate the field strength in the air and the dielectric). Could you recommend this arrangement if the breakdown strength of air is 3X10⁶ Vm^-1?

Question :5 (a) Derive an expression for the capacitance per unit length of a co-axial cable. Let the radii of the inner and outer conductors be r₁ and r₂ and let the insulation between them have relative permittivity ε_r.

(b) If r₁ =1 mm. r₂ = 9 mm and ε_r= 4.0 (oil impregnated paper), calculate the capacitance of 10 km of the cable. If the electric field strength in the insulation is not to exceed 20 kV/mm, find the maximum voltage which can be applied to the cable. Where is the insulation likely to begin to break down?

Question :6 a) The current through a 0.5 μF is shown in Figure. At t=0, the voltage is zero. Calculate and sketch the voltage, power, and stored energy to scale versus time.

[hint: v_c(t) = 1/c _t0∫^t(i_c(t) dt + v_c(t₀))]

Question :7 Using Gauss' Law, derive the value of the electrostatic E, field within a hollow charged metallic sphere.

[This relates to the early expriement performed by Cavendish which led to the reliasation that electric forces obeyed and "inverse-square law".]

Question :8

(a) Use node-voltage analysis to find v1.

(b) Write v1 in the time domain.