Assume a parallel plate capacitor in which paper layer is kept with
a goal of protecting conductors from one another. The insulator is
impregnated with oil to give it a £r. The oil used has a dielectric
strength Vo = 20,000 V/mm. Assume the thickness of insulator in
mm. For practical purposes of space, the insulator assembly is
rolled as on a ſpool and placed in a protective shell. Assume E is
unifarm between the conductor. Find
(a) The capacitance of the device.
(b) Find voltage rating of the capacitor for four different values of
thickness of insulator.
(c) Assume the insulator which is kept between two conductors is
getting damaged. It leads to change in dielectric strength. What will
be the voltage rating for different thickness of insulator?
Answers
Explanation:
A capacitor is a device used to store electric charge. Capacitors have applications ranging from filtering static out of radio reception to energy storage in heart defibrillators. Typically, commercial capacitors have two conducting parts close to one another, but not touching, such as those in Figure 1. (Most of the time an insulator is used between the two plates to provide separation—see the discussion on dielectrics below.) When battery terminals are connected to an initially uncharged capacitor, equal amounts of positive and negative charge, +Q and –Q, are separated into its two plates. The capacitor remains neutral overall, but we refer to it as storing a charge Q in this circumstance.
Part a of the figure shows a charged parallel plate capacitor and part b of the figure shows a charged rolled capacitor. In the parallel plate capacitor, two rectangular plates are kept vertically facing each other separated by a distance d. These two plates are the conducting parts of the capacitor. One plate is connected to the positive terminal of the battery, and the other is connected to the negative terminal of the battery. One plate has a positive charge, plus Q, and the other plate has a negative charge, negative Q. The rolled capacitor has conducting parts in the form of a spiral coil. Between the two conducting parts is insulating material, also in the form of a coil. The conducting and insulating materials of the capacitor are rolled together to form a spiral. The outer conducting coil is connected to the positive terminal of the battery, and the inner coil is connected to the negative terminal of the battery.