An uncharged capacitor with a solid dielectric is connected to a similar air capacitor charged to a potential of V0. If the common potential after sharing of charges becomes V, then the dielectric constant of the dielectric must be ?

Solution)
Capacitor or condenser, device for the storage of electric charge. Simple capacitors have two plates made of an electrically conducting material (e.g., a metal) and divided by a nonconducting material or dielectric (e.g., glass, paraffin, mica, paper, oil, tantalum, or air). The Leyden jar is a simple capacitor. If an electrical potential (voltage) is applied to the plates of a capacitor (e.g., by connecting one plate to the positive and the other to the negative terminal of a storage battery), the plates will become charged, one positively and one negatively. If the externally applied voltage is then removed, the plates of the capacitor remain charged, and the presence of the electric charge induces an electrical potential between the plates. This phenomenon is known as electrostatic induction. The capacity of the device for storing electric charge (i.e., its capacitance) can be increased by increasing the area of the plates, by decreasing their separation, or by changing the dielectric. The dielectric constant of a particular dielectric is the measure of the dielectric''s unit capacitance. It defines the ratio of the capacitance of a dielectric-filled capacitor to a capacitor of the similar size with a vacuum between the plates. Capacitors are used in many electrical and electronic devices. The main capacitor classifications are non-polarized (used for AC circuits) and polarized (used for DC circuits). Capacitors can also be classified as fixed or variable. One type of variable capacitor, formerly used in radio and television tuning circuits, consisted of two sets of semicircular plates, one fixed and the other mounted on a movable shaft. By rotating the shaft the area of overlap of the two plates increases or decreases, therefore increasing or decreasing the capacitance. These devices have largely been replaced by frequency synthesizers and a special type of solid-state diode, known as a varactor, whose capacitance changes with the reverse-biased voltage across it.