The Capacitor Capacitors and capacitance Lecture 6 - Capacitors Capacitors and capacitance The capacitor is a useful device for storing electrical energy (“storing charge”). Ewald Georg von Kleist, a German scientist invented the capacitor in November 1745. Several months later Pieter van Musschenbroek, a Dutch professor at the University of Leyden came up with a very similar device in the form of the Leyden jar, which is typically credited as the first capacitor. The Leyden jar consisted of a glass jar, half filled with water and lined inside and out with metal foil. LUIFP Semester 1 Basic Electricity

The Capacitor Lecture 6 - Capacitors LUIFP Semester 1 Basic Electricity

The Capacitor Lecture 6 - Capacitors The capacitor is a useful device for storing electrical energy (“storing charge”). It comprises two conducting plates in close proximity to each other. LUIFP Semester 1 Basic Electricity

Real capacitors How does it fit? Let’s Take one apart!

The Capacitor Lecture 6 - Capacitors A practical capacitor consists of two flexible conducting strips separated by an insulating layer rolled in a cylindrical tube The strips are like the metal plates of the parallel plate capacitor but they are much smaller in physical size. The maximum working voltage of a capacitor should never be exceeded. LUIFP Semester 1 Basic Electricity

The Capacitor V = e.m.f -q +q Lecture 6 - Capacitors When the capacitor is connected to a battery, equal and opposite charge flows onto the plates The current flows until the potential difference between them is the same as the battery’s e.m.f. V = e.m.f +q -q LUIFP Semester 1 Basic Electricity

The Capacitor Lecture 6 - Capacitors When you connect a capacitor to a battery, here's what happens: • The plate on the capacitor that is attached to the negative terminal of the battery accepts electrons that the battery is producing. • The plate on the capacitor that is attached to the positive terminal of the battery loses electrons to the battery. Once it's charged, the capacitor has the same voltage as the battery (1.5 volts on the battery means 1.5 volts on the capacitor). LUIFP Semester 1 Basic Electricity

The Capacitor – water tower analogy Lecture 6 - Capacitors When the capacitor is connected to a battery, charge flows onto the plates until the p.d. between them is the same as the battery e.m.f. A capacitor stores energy. Often said to store charge. Using water analogy, a capacitor is similar to a water tower which stores water energy produced by a water pump. LUIFP Semester 1 Basic Electricity

Capacitor versus battery Lecture 6 - Capacitors When a capacitor is charged, it stores electrical energy When a battery is charged it converts electrical energy from a charger into chemical energy and stores chemical energy. Battery usually stores much more energy than a capacitor, but energy from a battery cannot be released fast. LUIFP Semester 1 Basic Electricity

The Capacitor – applications Lecture 6 - Capacitors Therefore we should use a capacitor when we need a fast release of relatively small amount of energy, while a battery is useful if we need more energy which is slowly released. Sometimes, capacitors are used to store charge for high-speed use. That's what a flash does. Big lasers use this technique as well to get very bright, instantaneous flashes. Capacitors can also eliminate ripples. If a line carrying DC voltage has ripples or spikes in it, a big capacitor can even out the voltage by absorbing the peaks and filling in the valleys. A capacitor can block DC voltage. LUIFP Semester 1 Basic Electricity

The Capacitor A capacitor stores energy. Often said to store charge. Lecture 6 - Capacitors The capacitor is a useful device for storing electrical energy (“storing charge”). It comprises two conducting plates in close proximity to each other. When the capacitor is connected to a battery, equal and opposite charge flows onto the plates until the potential difference between them is the same as the battery e.m.f. A capacitor stores energy. Often said to store charge. LUIFP Semester 1 Basic Electricity

Dielectrics Lecture 6 - Capacitors In order to increase the amount of stored charge in a capacitor, a dielectric can be added between capacitor plates. An insulating material (dielectric) contains atoms with bound electrons. A positive charge attracts these electrons to one side of the atom, a negative charge repels them from the other, creating a dipole. LUIFP Semester 1 Basic Electricity

Dielectrics Lecture 6 - Capacitors A positive charge attracts these electrons to one side of the atom, a negative charge repels them from the other - creates a dipole. No charge, no electric field on a capacitor plate. Dipoles have random orientation. When some charge is stored on a capacitor, the electric field appears. Positive charges of dipoles are attracted to the negatively charged capacitor plate, while negative charges of dipoles are attracted to the positive capacitor plate. Therefore, dipoles orient along field lines. LUIFP Semester 1 Basic Electricity

Dielectrics Q - Charge on capacitor plates Lecture 6 - Capacitors The net effect is to reduce the effective surface charge on the plates, and so the capacitance increases, since the same charge on the capacitor plates produces weaker electric fields. In other words, oriented dipoles create the electric field pointed in the opposite direction with respect to the applied field (electric field created by the capacitor plate). -q - Charge induced by oriented dipoles Q - Charge on capacitor plates The capacitor “feels” smaller charge Q-q LUIFP Semester 1 Basic Electricity

Lecture 6 - Capacitors Dielectrics Field generated by capacitor plate E “Field” or polarization of dielectric P = 0 cr E where coefficient cr is called susceptibility, 0 permittivity of a vacuum The total field from capacitor plate and dielectric is related to 0 (1+cr) E or r0 E with the electric permitivity of a dielectric r =1+cr Therefore, the electrical permitivity of a vacuum is 0 and the permitivity of a dielectric is r0. Dielectrics reduce the effective charge on a capacitor plate and so increase capacitance. LUIFP Semester 1 Basic Electricity

Dielectrics Lecture 6 - Capacitors An insulating material (dielectric) contains atoms with bound electrons. A positive charge attracts these electrons to one side of the atom, a negative charge repels them from the other - creates a dipole. The net effect is to reduce the effective surface charge on the plates, and so the capacitance increases. The electrical permittivity of a vacuum is 0 and the permittivity of a dielectric is r0. Dielectrics reduce the effective charge on a capacitor plate and so increase capacitance. LUIFP Semester 1 Basic Electricity

Charging a Capacitor e- R1 R2>R1 Lecture 6 - Capacitors Charging a Capacitor R1 R2>R1 A capacitor is charged through a resistance. The larger the resistance, the longer it takes to charge. As charge flows onto the plates, a potential difference appears between the plates. Any relations between Q and V ? V e- +Q -Q LUIFP Semester 1 Basic Electricity

Charging a Capacitor – water analogy Lecture 6 - Capacitors Charging a Capacitor – water analogy V e- +Q -Q Yes, the stored charge is proportional to the voltage difference between capacitor plates. Water tank analogy: capacity or volume of a water reservoir is analogous to the capacitance of a capacitor. The value of capacitance is defined as the amount of charge on each plate when it has reached the battery e.m.f. divided by that e.m.f. C is measured in farads. LUIFP Semester 1 Basic Electricity

Charging a Capacitor – capacitance in farads Lecture 6 - Capacitors Charging a Capacitor – capacitance in farads 1 farad is the capacitance of a capacitor which can store 1 coulomb if a voltage of 1 Volt is applied to its plates. A 1 farad capacitor can store 6.25 x 1018, or 6.25 billion billion electrons if 1 volt is applied. One amp represents a rate of electron flow of 1 coulomb of electrons per second, so a 1 farad capacitor can hold 1 amp current during 1 second at 1 volt. A 1-farad capacitor would typically be pretty big: the planet Earth: about 710 μF. For this reason, capacitors are typically measured in microfarads. Q=+1C =1V Q=-1C 710 μF LUIFP Semester 1 Basic Electricity

Farad: battery versus capacitor Lecture 6 - Capacitors A standard alkaline AA battery holds about 2.8 amp-hours. That means that a AA battery can produce 2.8 amps for an hour at 1.5 volts (about 4.2 watt-hours – a AA battery can light a 4-watt bulb for a little more than an hour). To store one AA battery's energy in a capacitor at 1 volt, you would need 3,600 s x 2.8 amps / 1 Volt = 10,080 Farads to hold it, because an amp-hour is 3,600 amp-seconds. 10,080 Farads is going to take up a LOT more space than a single AA battery! Obviously, it's impractical to use capacitors to store any significant amount of power. LUIFP Semester 1 Basic Electricity

Charging a Capacitor C is the symbol for capacitance C=Q/V Lecture 6 - Capacitors Charged through a resistance. The larger the resistance, the longer it takes to charge. As charge flows onto the plates, a potential difference appears between the plates. The value of capacitance is defined as the amount of charge on each plate when it has reached the battery e.m.f. divided by that e.m.f. C is measured in Farads. C is the symbol for capacitance C=Q/V Unit is the Farad (F) LUIFP Semester 1 Basic Electricity

Parallel Plate Capacitor Lecture 6 - Capacitors Consider two parallel metal plates of the same area. Larger area plates means more charge can be stored on each. Closer together plates give stronger attraction between the opposite charges, so more charge can be stored. LUIFP Semester 1 Basic Electricity

Parallel Plate Capacitor Lecture 6 - Capacitors Consider two parallel metal plates of the same area. Larger area plates means more charge can be stored on each. Closer together plates give stronger attraction between the opposite charges, so more charge can be stored. 𝐶 ∝ 𝐴 𝑑 seems reasonable? LUIFP Semester 1 Basic Electricity

Parallel Plate Capacitor Lecture 6 - Capacitors Consider two parallel metal plates of the same area. The larger dielectric constant of the material in between the more charge can be stored. It can be shown that: LUIFP Semester 1 Basic Electricity

Parallel Plate Capacitor Lecture 6 - Capacitors Relative permittivity No units 1 for air or vacuum Permittivity of Free Space. (Constant). ε0 Value is given on formula sheet ε0 =8.85 * 10 -12 Fm -1 LUIFP Semester 1 Basic Electricity

Parallel Plate Capacitor Lecture 6 - Capacitors A capacitor comprises two discs of metal 20 cm in diameter that are 0.5 mm apart. It’s filled by polythene (er=2.3) between plates. The permittivity of free space e0=8.85x10-12 Fm-1. Calculate capacitance of the capacitor and the charge on each plate when connected to a 1.5 V battery. How long can this capacitor keep 2.0 A current? The diameter is 0.2m, the distance between plates is 5x10-4m. The areas of plates are A=pd2/4 = 3.14x0.22/4=3.14x10-2 m2. C=8.85x10-12x2.3x3.14x10-2/(5x10-4) [Fxm-1xm2/m] = 13x10(-12-2-(-4))[Fm(-1+2-1)]= 13x10-10[F]=1.3x10-9 F. To find the charge we use Q=CV=1.3x10-9F x 1.5V = 2.0x10-9C. I=Q/t, thus, t=Q/I = 2.0x10-9C/2.0A = 10-9s = 1ns It can be shown that: 10-9 nano n LUIFP Semester 1 Basic Electricity

Parallel Plate Capacitor Lecture 6 - Capacitors Consider two parallel metal plates of the same area. Larger area of the plates means more charge can be stored on each. Closer together plates give stronger attraction between opposite charges, so more charge can be stored. The larger the dielectric constant of the material in between, the more charge can be stored. It can be shown that: The capacitance of a parallel plate capacitor is C=A0 r/d LUIFP Semester 1 Basic Electricity