Electric Capacitance Physics Lesson 25 by Owen Borville 12.26.2025
A capacitor is a device used to store electric charge and electric energy. The amount of charge Q a vacuum capacitor can store depends on two major factors: (1) the voltage applied and (2) the capacitor's physical characteristics, such as its size and geometry. The capacitance C is the amount of charge stored per volt, or Capacitance = Q (charge)/V (volt) = C = Q/V.
The capacitance of a capacitor is a measure of how much charge can be stored in the capacitor per unit potential difference between its plates. Capacitance of a system of conductors depends only on the geometry of their arrangement and physical properties of the insulating material that fills the space between the conductors. The unit of capacitance is the farad, where 1 F = 1 C/1V.
When several capacitors are connected in a series combination, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances. When several capacitors are connected in a parallel combination, the equivalent capacitance is the sum of the individual capacitances. When a network of capacitors contains a combination of series and parallel connections, series and parallel networks are identified and their equivalent capacitances are calculated step by step until the entire network becomes reduced to one equivalent capacitance.
The capacitance of a parallel plate capacitor is C = ε0 A/d, when the plates are separated by air or free space. ε0 is called the permittivity of free space. A parallel plate capacitor with a dielectric between its plates has a capacitance of C = κε0A/d, where κ is the dielectric constant of the material. The maximum electric field strength above which an insulating material begins to break down and conduct is called dielectric strength.
The total capacitance in a series is 1/Cs = 1/C1 + 1/C2 + 1/C3 + ... Total capacitance in parallel Cp = C1 + C2 + C3 + ... If a circuit contains a combination of capacitors in a series and parallel, to find the capacitance, identify series and parallel parts, compute their capacitances, and then find the total.
The capacitance of a vacuum spherical capacitor is C = Q/V = 4πε0R1R2/R2-R1 The capacitance of a vacuum cylindrical capacitor is C = Q/V = 2πε0l/ln(R2/R1)
Capacitors are used to supply energy in a variety of devices, including defibrillators, microelectronics such as calculators, and flash lamps, to supply energy. The energy stored in a capacitor is the work required to charge the capacitor, beginning with no charge on its plates. The energy is stored in the electric field in the space between the capacitor plates and it depends on the amount of electrical charge on the plates and on the potential difference between the plates. The energy stored in a capacitor network is the sum of the energies stored on individual capacitors in the network and it can be calculated as the energy stored in the equivalent capacitor of the network.
The energy stored in a capacitor can be expressed in three ways, as Ecap = QV/2 = CV^2/2 = Q^2/2C where Q is the charge, V is the voltage, and C is the capacitance of the capacitor. The energy is in joules when the charge is in coulombs, voltage is in volts, and capacitance is in farads. The energy density can be calculated as uE = ε0E^2/2
The capacitance of an empty capacitor is increased by a factor of κ when the space between its plates is completely filed by an dielectric with dielectric constant κ. Each dielectric material has its specific dielectric constant. The energy stored in an empty isolated capacitor is decreased by a factor of κ when the space between its plates is completely filled with a dielectric with dielectric constant κ while disconnecting the battery and keeping the charge on the capacitor constant.
The capacitance of a capacitor with dielectric is C = κC0 The energy stored in an isolated capacitor with a dielectric is U = 1/κU0 The Dielectric constant is κ = E0/E The induced electrical field in a dielectric is Ei = (1/κ-1)E0
When a dielectric is inserted between the plates of a capacitor, equal and opposite surface charge induced on the two faces of the dielectric. The induced surface charge produces an induced electrical field that opposes the field of the free charge on the capacitor plates. The dielectric constant of a material is the ratio of the electrical field in vacuum to the net electrical field in the material. A capacitor filled with dielectric has a larger capacitance than an empty capacitor. The dielectric strength of an insulator represents a critical value of electrical field at which the molecules in an insulating material start to become ionized. When this happens, the material can conduct and dielectric breakdown is observed.
A capacitor is a device used to store electric charge and electric energy. The amount of charge Q a vacuum capacitor can store depends on two major factors: (1) the voltage applied and (2) the capacitor's physical characteristics, such as its size and geometry. The capacitance C is the amount of charge stored per volt, or Capacitance = Q (charge)/V (volt) = C = Q/V.
The capacitance of a capacitor is a measure of how much charge can be stored in the capacitor per unit potential difference between its plates. Capacitance of a system of conductors depends only on the geometry of their arrangement and physical properties of the insulating material that fills the space between the conductors. The unit of capacitance is the farad, where 1 F = 1 C/1V.
When several capacitors are connected in a series combination, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances. When several capacitors are connected in a parallel combination, the equivalent capacitance is the sum of the individual capacitances. When a network of capacitors contains a combination of series and parallel connections, series and parallel networks are identified and their equivalent capacitances are calculated step by step until the entire network becomes reduced to one equivalent capacitance.
The capacitance of a parallel plate capacitor is C = ε0 A/d, when the plates are separated by air or free space. ε0 is called the permittivity of free space. A parallel plate capacitor with a dielectric between its plates has a capacitance of C = κε0A/d, where κ is the dielectric constant of the material. The maximum electric field strength above which an insulating material begins to break down and conduct is called dielectric strength.
The total capacitance in a series is 1/Cs = 1/C1 + 1/C2 + 1/C3 + ... Total capacitance in parallel Cp = C1 + C2 + C3 + ... If a circuit contains a combination of capacitors in a series and parallel, to find the capacitance, identify series and parallel parts, compute their capacitances, and then find the total.
The capacitance of a vacuum spherical capacitor is C = Q/V = 4πε0R1R2/R2-R1 The capacitance of a vacuum cylindrical capacitor is C = Q/V = 2πε0l/ln(R2/R1)
Capacitors are used to supply energy in a variety of devices, including defibrillators, microelectronics such as calculators, and flash lamps, to supply energy. The energy stored in a capacitor is the work required to charge the capacitor, beginning with no charge on its plates. The energy is stored in the electric field in the space between the capacitor plates and it depends on the amount of electrical charge on the plates and on the potential difference between the plates. The energy stored in a capacitor network is the sum of the energies stored on individual capacitors in the network and it can be calculated as the energy stored in the equivalent capacitor of the network.
The energy stored in a capacitor can be expressed in three ways, as Ecap = QV/2 = CV^2/2 = Q^2/2C where Q is the charge, V is the voltage, and C is the capacitance of the capacitor. The energy is in joules when the charge is in coulombs, voltage is in volts, and capacitance is in farads. The energy density can be calculated as uE = ε0E^2/2
The capacitance of an empty capacitor is increased by a factor of κ when the space between its plates is completely filed by an dielectric with dielectric constant κ. Each dielectric material has its specific dielectric constant. The energy stored in an empty isolated capacitor is decreased by a factor of κ when the space between its plates is completely filled with a dielectric with dielectric constant κ while disconnecting the battery and keeping the charge on the capacitor constant.
The capacitance of a capacitor with dielectric is C = κC0 The energy stored in an isolated capacitor with a dielectric is U = 1/κU0 The Dielectric constant is κ = E0/E The induced electrical field in a dielectric is Ei = (1/κ-1)E0
When a dielectric is inserted between the plates of a capacitor, equal and opposite surface charge induced on the two faces of the dielectric. The induced surface charge produces an induced electrical field that opposes the field of the free charge on the capacitor plates. The dielectric constant of a material is the ratio of the electrical field in vacuum to the net electrical field in the material. A capacitor filled with dielectric has a larger capacitance than an empty capacitor. The dielectric strength of an insulator represents a critical value of electrical field at which the molecules in an insulating material start to become ionized. When this happens, the material can conduct and dielectric breakdown is observed.