An air capacitor is made by using two flat plates, each with area A, separated by a distance d. Then a metal slab having thickness a (less than d) and the same shape and size as the plates is inserted between them, parallel to the plates and not touching either plate (Fig. P24.62). (a) What is the capacitance of this arrangement? (b) Express the capacitance as a multiple of the capacitance C0 when the metal slab is not present. (c) Discuss what happens to the capacitance in the limits

Solution 66P Step 1 of 9: The capacitor is a device used to store electrical energy in a confined region and also which is capable of releasing the electrical energy instantly. The capacitance of the capacitor is the capability of the capacitor to store the charge or electrical energy. Step 2 of 9: Before inserting the dielectric medium(initial) Consider two parallel plates at d distance apart. with air between them, having capacitance C. Under a potential difference V as in figure below, Capacitance is, 0 A C = d .............1 Where is the permittivity of free space , A is the area of the parallel plates and d is the 0 distance between them. Step 3 of 9: After inserting dielectric medium, For the same above configuration, we are inserting a dielectric medium which is having a dielectric constant K as shown below, Capacitance is, KA C di = 0 .....................2 d Where i0 the permittivity of free space , K = dielectric constant of medium, A is the area of the parallel plates and d is the distance between them. Step 4 of 9: (a) What is the capacitance of this arrangement In the given problem, the two plates with area A each at distance d apart. A metal slab having the thickness a is inserted between them as shown in the figure below. Here we need to calculate the net capacitance of the arrangement. Step 5 of 9: From above figure, we can see that; there are two capacitor in series. One being the capacitor with thickness (d-a) without dielectric and the other capacitor with thickness a with dielectric medium. In order to calculate the net capacitance, we need to first calculate the individual capacitance. Capacitance of capacitor without dielectric, Using equation 1, C = 0A without dielectrda Capacitance of capacitor with dielectric medium, KA Using equation 2, C = 0 dielectric a