Capacitance PHY 232 Introduction: The purpose of this experiment is to explore basic concepts related to capacitance by investigating how the capacitance of a parallel-plate capacitor varies when the plate separation is changed or when the plate area is changed. Other capacitance related parameters, such as stored charge and stored energy. are also examined. Theory: Capacitors store charge. A capacitor can be made with any two conductors kept insulated from each other. If the conductors are connected to a potential difference, V, as for example the opposite terminals of a battery, then the two conductors are charged with equal but opposite amounts of charge Q, which is then referred to as the \"charge in the capacitor\". The actual net charge on the capacitor is zero. The capacitance of the device is defined as the amount of charge Q stored in each conductor divided by the potential difference V applied: c=Qv Rearranging gives: V=Q/C Eq. (1) Plate area, 4 A simple form of a capacitor consists of two parallel conducting plates, each with area A, separated by a distance d. The charge is uniformly distributed on the surface of the plates. The capacitance of this parallel-plate capacitor is given by: C =kEAd where K is the dielectric constant of the insulating matenal between the plates (k = 1 for vacuum); other values are measured experimentally and can be found in tables), and gp is the permmittivity constant, of universal value ,=8.654 x 10" F/m. The Sl unit of capacitance is the Farad (F). In a capacitance testing system there could be additional capacitance due to the measurement device and the connecting wires. Sometimes the additional capacitance, which we denote as C,., cannot be ignored. Including this capacitance, as a capacitor in parallel with the parallel-plate capacitor being tested, gives: C = KEgA/d + Cyys Eq. (2) where Csys is the capacitance of the rest of the system (spurious capacitance). Substitution of Equation 2 into Equation 1 yields: V = Q/[KEA/D + Cyys) Eq. (3) An insulating material placed between the plates of a capacitor will increase its capacitance by a factor k called the dielectric constant: C=kGCy Eq. (4) with Cq = 0A/d being the capacitance when there is vacuum between the plates of the capacitor. Dielectric materials are non-conductive. Any dielectric material can be used to keep the plates in a capacitor insulated from each other (preventing them from touching and discharging). To three significant figures, k = 1.00 for air. For all other materials, k > 1. If the charge on a capacitor is kept constant while a dielectric is inserted between the plates (the capacitor is not connected to a voltage source), Equations 1 & 4 yield: Q=CV=CVyg=(Cik)Vy so V=Vyk Where V; is the voltage before inserting the dielectric and V is the voltage after insertion. Since k > 1 always, we have: V