CAPACITOR BASICS OBJECTIVE ๏ฑUnderstand that capacitance is defined as C =Q/V and be able to use this equation. ๏ฑBe able to use the equation W = 1/2 QV for the energy stored by a capacitor, be able to derive the equation from the area under a graph of potential difference against charge stored and be able to derive and use the equations W = 1/2 ๐ช๐ฝ๐ and W= ๐ ๐ ๐ธ๐ /๐ช https://www.youtube.com/watch ?v=L6cgSxpGmDo ๏ฑ A Capacitor is a two-terminal, electrical component used to store store electrical energy . . ๏ฑ Along with resistors and inductors, they are one of the most fundamental components we use in a circuit. Capacitance The ability of any object to โstoreโ electric charge is described as capacitance. An electrical component designed to have significant capacitance is called a capacitor. Capacitors are useful components of circuits because of their ability to store small amounts of energy. Parallel plate capacitors Parallel metallic plates separated by an insulator are the most common kind of capacitor. When a p.d. is connected across the plates they will gain equal and opposite charge. https://www.youtube.com/watch?v=f_MZNsEqy Qw CHARGING OF CAPACITOR When the power supply is connected, electrons flow from negative terminal to positive terminal. Electrons cannot cross the gap between the plates so they build up in plate B connected to negative terminal. A B https://www.youtube.com/watch?v=f_MZNsEqy Qw CHARGING OF CAPACITOR Electrons in plate B repel the electrons in the plates A connected to the positive terminal and makes the electrons flow towards the positive of the battery. Now plate A become positively charged and plate B is negatively charged. A B https://www.youtube.com/watch?v=f_MZNsEqy Qw CHARGING OF CAPACITOR ๏ถ Electrons in plate B repel the electrons in the plates A connected to the positive terminal and makes the electrons flow towards the positive of the battery. ๏ถ Now plate A become positively charged and plate B is negatively charged. A B https://www.youtube.com/watch?v=f_MZNsEqy Qw CHARGING OF CAPACITOR ๏ถ The attraction between the opposite charges across the gap creates an electric field between the plates. ๏ถ This process of this charging stops when p.d. across the plates has risen to become equal to the p.d. across the battery. A B https://www.youtube.com/watch?v=f_MZNsEqy Qw CHARGING OF CAPACITOR ๏ถ At this stage the capacitor is acting like a store of charge. A B Only charge a capacitor to or below its specified voltage rating. Charging a capacitor to a voltage beyond its voltage rating can destroy the capacitor. https://www.youtube.com/watch?v=X5bzjs3ByBU Discharging of capacitor occurs when charged capacitor is connected to a load in a circuit. Calculating capacitance ๏ถ The amount of charge a capacitor can store, per ๐ธ volt across it is called as its capacitance. C = ๐ฝ ๏ถ 1F = 1J / 1V ๏ถ Capacitance is measured in farads(F) ๏ถ This is a large unit, so that ฮผF and pF are in common use in practical lab works. ๏ถ The capacitance of parallel plates increases if the plates have larger area and are closer together. Adding a suitable insulator, with high permittivity, between the plates also increases capacitance. Effect of insulators in a capacitor A capacitor with a an insulators stores the same charge as one without an insulators, but at a lower voltage. Therefore a capacitor with a insulators in it is more effective. Charging a capacitor In this case, the capacitor charges up to 9 volts, since it's connected to a 9-volt battery. Many of the times while charging a capacitor, a resistor is used in series with the capacitor and voltage source to decrease the amount of current that flows through the capacitor, so that the capacitor isn't damaged. This is usually recommended. ๏ฑ 3× ๐๐๐ F ๏ฑ 3.6× ๐๐๐ ๐ช Coulomb meter A Coulomb meter is a tool for measuring the electrostatic charge of a material. https://www.youtube.com/watch ?v=5hFC9ugTGLs https://www.youtube.com/watch ?v=X4EUwTwZ110 There are other versions of this formula. Since Q = CV, we get Ue = (1/2)CV2. Also, Ue = (1/2)QV. 1.7× 10โ5 F 1.0× 10โ3 ๐น 1.1× 10โ3 ๐ Capacitor discharge curves ๏ฑ Unless it is required to discharge a capacitor very quickly, a resistor will be included in any capacitor circuit in order to control the rate of discharging (or charging). ๏ฑ The charging or discharging of a capacitor can be observed and recorded by measuring either the changing p.d. across it, or the changing current through the resistor. When a capacitor discharges, the rate of discharge will be highest at the beginning because the amount of charge on the plates is greatest, so that the free electrons experience the greatest forces. Figure shows a typical discharge graph. Note that it may represent the variation with time of the discharge current, or the voltage acros the capacitor, or the charge remaining on the capacitor plates During a capacitor discharge, the charge, voltage and current decrease exponentially. That is, their values fall by the same fraction in equal time intervals. The rate of discharge at any time (which could be determined from the gradient of the graph at that moment) is proportional to the value of the quantity at that moment. For example, - ฮQ/โ๐ โ Q. Current: Initially, the electric field from the supply sends a large surge of electrons onto the capacitor, so the current starts at its maximum. After a little time, the electrons already stored on the capacitor reduce the effective push (or electric field) from the supply, so the charge movement is reduced โ a smaller current. Eventually, the capacitor has as much charge as the 6 V supply can push onto it, and the mutual repulsion of electrons already stored stops any further charge moving onto the capacitor; the current falls to zero. Potential difference(p.d): Initially, the capacitor has no charge on it, so its p.d. is zero. After a little time, the charge stored across the capacitor creates some p.d., which could be measured using a voltmeter. Eventually, the capacitor has as much charge as the 6 V supply can push onto it, which will be when it has also reached a voltage of 6 V, and it will remain at this value. Charge: Initially, the capacitor has no charge on it. The current starts at its maximum so, after a little time, some charge is stored on the capacitor. The reduced current continues to add charge to the capacitor but at a slower rate. Eventually, when the current reaches zero, no more charge is added to the capacitor, and the amount on it remains constant at its maximum, CV Basic exponential decay curve as per fig B(a): initial current is 0.6 mA. This should fall to 0.22 mA in 0.5 s. At 1 s, the current has dropped to 0.08 mA, then at 1.5 s it is 0.03 mA, finishing at 0.01 mA by 2 s. Depending on scale, it is likely that the final half second should look horizontal along zero mA. How could we make light lamp for longer , for longer given the same power supply? ๏ฑ Store more charge on the capacitor ๏ฑ Decrease the rate at which the capacitor discharge. ๏ฑ Increase the capacitance C, will increase the charge stored . Q=CV ๏ฑ The charge will flow more slowly if the bulb resistance R is greater. Time constant Rate of change of a capacitor can be gained by working out time constant (๐) ๐ = ๐น๐ช Time constant in C-R circuit tells us how many seconds it takes for the current to fall to 37% of its starting value. Time constant determines how long it takes for a capacitor to change or discharge over one time constant. A 15ฮผF-capacitor is connected to a 9.6-V battery. Calculate (a) the charge accumulation and (b) the energy stored in it (a) Q = CV ; Q = (15ฮผF)(9.6 V) = 144ฮผC (b) Ue = (1/2)QV ; Ue = (1/2)(144ฮผC )(9.6V) = 690 ฮผJ Capacitor Discharge Equation Derivation