Capacitors charges in a predictable way, and it takes time for the capacitor to charge. 0 0 Similar questions When the charge given to a capacitor is doubled its capacitance Medium View solution > A capacitor is charged with a battery and then removed from the battery. The formula V=QC gives the amount of charge that is there on one of the plates. and the charge on the capacitor is = Qmax = C. This circuit will have a maximum current of I max = A. just after the switch is closed. Asking for help, clarification, or responding to other answers. Skip to content Home Blog Because for the sudden changes in voltage(which would probably be at the time of start of charging and discharging ) the capacitor acts as short circuit. Thanks for contributing an answer to Physics Stack Exchange! Some of these circuits could be charged in less than 20 seconds and hold the charge for up to 40 minutes while having relatively large capacitances of up to 100 milliFarads (mF). (2). (1), , plug them into equation (1) (2) In equation (2), the only independent variable is time t, and C, E are fixed values. After a time of 5T the capacitor is now said to be fully charged with the voltage across the capacitor ( Vc ) being aproximately equal to the supply voltage ( Vs ). 2003-2022 Chegg Inc. All rights reserved. The best answers are voted up and rise to the top, Not the answer you're looking for? Where did the $2\sqrt{3}$ come from? Maximum Voltage Every capacitor has a maximum voltage that it can handle. Capacitor Charge and Time Constant Calculator This calculator computes for the capacitor charge time and energy, given the supply voltage and the added series resistance. In an oscillating LC circuit the maximum charge on the capacitor is 2.2 C and the maximum current through the inductor is 7.5 mA. The angular frequency of the LC circuit is given by Equation 14.6. Thus, the charge on the capacitor will become zero only after infinite time. For maximum life, capacitors usually need to be able to handle the maximum amount of reversal that a system may experience. Figure 2. For circuit parameters: R = , V b = V. C = F, RC = s = time constant. It only takes a minute to sign up. What is the name of this battery contact type? Is there any limit on the maximum charge we can store in it? Definition:The time required to charge a capacitor to about 63 percent of the maximum voltage in an RC circuit is called the time constant of the circuit. For a better experience, please enable JavaScript in your browser before proceeding. Charging the Capacitor with a Resistor Power Supply Voltage, Volts Resistor, Ohms Capacitor Value, microFarads Charging Time, milliseconds Calculation precision Part (a) What is the period of the circuit's oscillation, in seconds? In order to maximise the charge that a capacitor can hold, the dielectric material needs to have as high a . The polarity of stored charge can beeither negative or positive.Such as positive charge (+ve) on one plate and negative charge (-ve) on another plate of the capacitor. Capacitors with very low loss: cryogenic vacuum-gap capacitors. Net charge on capacitor is always zero because there is equal and unlike charges on plates. When the migration is complete, you will access your Teams at stackoverflowteams.com, and they will no longer appear in the left sidebar on stackoverflow.com. (a) the time constant of the circuit, (b) the maximum charge on the capacitor, and (c) the charge on the capacitor at a time equal to one time constant after the battery is connected. In an oscillating LC circuit, the maximum charge on the capacitor is 9.0 x 107 C and the maximum current through the inductor is 7.5 mA. The charges 1,257 views Jul 5, 2020 19 Dislike Share Doubtnut 2.09M subscribers In an oscillating LC circuit the. During the oscillations the maximum current in the inductor is. where A is the area of the plates in square metres, m 2 with the larger the area, the more charge the capacitor can store. The result can be a momentary spark, permanent damage to the dielectric, or even an explosion. Now, using the equation for the charging capacitor, V (t) = V s (1 - e -t/), we get the voltage across the . Convert the rms current to maximum current by multiplying it by the square root of two. AbstractThe charge phenomena under sine and halfwave sine voltages within the frequency range of 500 Hz are studied here. For b) I have a feeling Qmax for the capacitor will be Qmax = CV where V is the voltage across R2 since R2 and C are parallel, but I can't figure out V across R2 in terms of E, R1, R2, C. Can anyone help? S (b) How much time (in s) elapses between an instant when the capacitor is uncharged and the next instant when it is fully charged? For a vacuum dielectric, the Schwinger limit is about $1.3\cdot 10^{18}\rm{V/m}$ - ignoring all other sources of field emission (see for example the extensive description of Fowler-Nordheim analysis in this article on field emission, you cannot maintain this electric field (note - it is orders of magnitude higher than any realistic field you will ever maintain). After a point, the capacitor holds the maximum amount of charge as per its capacitance with respect to this voltage. Then using equation-2 we get, Energy stored = 1/2 (QV) = (23)2 = 3 Joule. How much charge is on each plate of the capacitor? What will be the maximum energy stored in the parallel plate capacitor? Besides its use in storing charge, a capacitor Is a key element of most a.c. circuits. Calculate difference between dates in hours with closest conditioned rows per group in R. Why did The Bahamas vote against the UN resolution for Ukraine reparations? Experts are tested by Chegg as specialists in their subject area. The charge will approach a maximum value Qmax = C. Can we prosecute a person who confesses but there is no hard evidence? Fun fact -- if you deplete a metal capacitor plate out of "all its charges" (so much as removing even just "one electron per atom") it simply will explode in gaseous poof of metallic ions! How do you find the maximum and minimum current? just after the switch is closed. Literature guides Concept explainers Writing guide . Derive an expression for the . When the electric field magnitude in the capacitor is zero which is true about the magnetic field magnitude in the inductor? Thanks again. . If the capacitor was 1000 microfarads, it would take 50 seconds in total. Also, if you permit "thick-enough" plates, you can probably then extract enough electrons from the material to exceed the surface $\sigma_max=23\,MC/m^2$, although those plates will probably lose their integrity as well, as extracting one electron from every copper atom will result in some weird material comprised entirely of $\text{Cu}^+$ ions likely to simply "explode" on itself over all that electrostatic repulsion! Set q(t) = to 99.9% of this value and solve for the corresponding time. What is the maximum charge of the capacitor? The capacitance of a capacitor can be defined as the ratio of the amount of maximum charge (Q) that a capacitor can store to the applied voltage (V). this occurs when the electric field between the plates exceeds about 3.0\\times10^6 \\space v/m3.010 6 v/m. For an example of this in practice, see. d is the distance or separation between the two plates. Medium View solution > In a series RC circuit having battery of 12 V, Potential drop across capacitor is charged from 0 to 6 V in 0.1 s. Find value of resistance R. @Floris fair enough, though I don't think there's a realistic experiment that will show this behaviour. Convert the rms current to maximum current by. The amount of charge Q a capacitor can store depends on two major factors. Figure 5.47 shows the flash bulb circuit of a single-use disposable camera. This effect is not a catastrophic breakdown, and it is easily modelled as the capacitor having a small component of resistive reactance. The batteries of the camera charge the inductor continuously. What defines the maximum charge a capacitor can store? So, the voltage drop across the capacitor is increasing with time. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Hence it draws more current. It typically stores 10 to 100 times more energy per unit volume or mass than electrolytic capacitors, can accept and deliver charge much faster than batteries, and tolerates many more charge and discharge cycles than rechargeable batteries. First note that as time approaches infinity, the exponential goes to zero, so the charge approaches the maximum charge \(Q = C\epsilon\) and has units of coulombs. Equivalent Series Resistance (ESR) Like any other physical material the terminals on a capacitor have a very tiny amount of resistance. . Because for the sudden changes in voltage. 14. Step 1 With the switch S open, there is no charge on the plates of the capacitor. Capacitors do not store charge. The currents will be a little higher with a 12V supply. The capacitance of a capacitor can be defined as the ratio of the amount of maximum charge (Q) that a capacitor can store to the applied voltage (V). S (b) How much time (in s) elapses between an instant when the capacitor is uncharged and the next instant when it is fully charged? Hence, I need to know the maximum amperage each capacitor can deliver so I can determine the number of capacitors needed in parallel to deliver the required power. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. rev2022.11.16.43035. As the maximum charge on the capacitor in the LC oscillation circuit is Q o. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Physics E&M: Ch 39.1 Capacitors & Capacitance Understood (24 of 27) Maximum Charge=? How do we know "is" is a verb in "Kolkata is a big city"? Example: In an L-C circuit L=85.0mH and C=3.20F. To learn more, see our tips on writing great answers. More specifically the effect of an electric current is to increase the charge of one plate of the capacitor and decrease the charge of the other plate by an equal amount. What is the maximum charge on the capacitor LC circuit? First week only $4.99! Answer: In this case, the ac capacitor is in charging mode. This quantity is known as the time constant: How do you find the maximum charge stored in a capacitor? What is the maximum possible value of voltage across the capacitor? Simply find the maximum of this function. The inductive reactance equals 6.28, The formula V=QC gives the amount of charge that is there on one of the plates. This can therefore store 270000 Coulombs., How do you calculate the charge on a capacitor? EM Field and Photons, Super capacitor 500F 2.7V Charge and Discharge Testing, Charge on a Capacitor is Proportional to Voltage and Capacitance, What Are The Characteristics Of Planet Earth That Makes It Habitable. Capacitor Charge Calculation just after the switch is closed. The formula for finding the current while charging a capacitor is: I = C d V d t The problem is this doesn't take into account internal resistance (or a series current-limiting resistor if you include one) or if the capacitor already has some charge. You have already calculated the total resistance RT so you can calculate the maximum voltage across the network of resistors straight away using. Polypropylene for example usually have max dV/dt specified and you can get 'pulse' versions of electrolytics for things like flashguns too. What is the maximum charge on the capacitor? Texas Instruments show that the typical output current of a CD4047 with a 10V supply is 10mA into a short circuit when the capacitor is beginning to charge and is. Capacitors play a significant role in the family of passive electronic components, and their uses are . The charges that accumulate on the plates of a capacitor are not provided by the material of the plates themselves but by the source that is charging them, so there is in principle no limit to the amount of charge that they can hold, if your source is strong enough. An LC circuit also called a resonant circuit tank circuit or tuned circuit is an electric circuit consisting of an inductor represented by the letter L and a capacitor represented by the letter C connected together. for finding minimum current you have to put the resistor in series. Part (a) What is the period of the circuits oscillation, in seconds? The ability of a capacitor to store maximum charge (Q) on its metal plates is called its capacitance value (C). Making statements based on opinion; back them up with references or personal experience. We say that we can charge a capacitor in proportion to the potential difference we apply across its plates and the maximum potential difference depends on the dielectric strength of the medium. The failure mode that you do get on a vacuum capacitor is leakage, which is caused by thermal electrons jumping out of the cathode and getting snatched by the electric field in the middle. and the charge on the capacitor is = Qmax = C. If I1 is the smallest current then the currents through the parallel resistors are guaranteed to be smaller than their maximums. Why do many officials in Russia and Ukraine often prefer to speak of "the Russian Federation" rather than more simply "Russia"? Part (a) What is the period of the circuits oscillation, in seconds? Inserting a dielectric in a parallel-plate capacitor. Supercapacitors are polar devices, meaning they have to be connected to the circuit the right way, just like electrolyte capacitors. If your reduce the air density between them, though, this mode becomes less and less effective, and at a good enough vacuum it will stop altogether. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. For an approximation, you can use the maximum rated voltage: Sponsored by RAID: Shadow Legends So as the capacitor size increases . The maximum-charge limits on actual physical capacitors are dictated by the dielectric breakdown of the medium between the plates, which typically is an insulating dielectric of some kind - common materials are paper, plastic, glass, mica and ceramics, as well as air and vacuum. When the capacitor fully charged the voltage across the capacitor will be equal to supply voltage? Answer: 2.21 10^11 C or. Maximum Voltage Every capacitor has a maximum voltage that it can handle. Part (b) What is the time interval, in seconds, between an instant when the capacitor is uncharged and the next instant when it is fully charged? The charge will approach a maximum value Qmax = C. because current is inversely proportional to resistance . Some of these circuits could be charged in less than 20 seconds and hold the charge for, Audioguru. It may not display this or other websites correctly. How tall should a bluebird house pole be. Why do you regard R1 and R2 as being in parallel? When the electric field magnitude in the capacitor is maximum which is true about the magnetic field magnitude in the inductor? Also, shouldn't the electric field inside the capacitor simply be $E = \sigma/\varepsilon_0$, without the factor of $1/2$ ? capacitor charge maximum S. sozener1. For a circuit model incorporating resistance see RLC circuit. A charged capacitor is connected to an ideal inductor to form an LC circuit with a frequency of oscillation f = 1.6 Hz. It is found that the selection of a 186 pF protection capacitor and a 333 k protection resistor can ensure that the actual voltage applied . At time t = s = RC. We review their content and use your feedback to keep the quality high. (a) What is the period of the oscillations (in s)? Maximum charge on capacitor after switch is closed is A 2 CE B 4 CE C 6 CE D 7 CE Medium Solution Verified by Toppr Correct option is A) Was this answer helpful? What is the charge on the capacitor when fully charged? Answer: 2.21 10^11 C or 1.38 108 e. please help find the answer step by step. Start your trial now! Theoretically, there is no limit as long as you can increase voltage: Capacitors typically cannot withstand this regime without being damaged, so the maximum viable charge will correspond to voltages lower than breakdown voltage. (a) What is the period of the oscillations (in s)? Therefore. Both of them are oppositely charged. Stack Exchange network consists of 182 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Maximum Charge On Capacitor Commercially available ultracapacitors can go to 5000 Farads, ratrd 2.7 V . (March - 2012) a) What are the factors on which the capacitance of a parallel plate air capacitor depends? The expressions for charge, capacitance and voltage are given below. C C\varepsilon \rightarrow C is the maximum charge on the capacitor, and hence can be denoted as q m a x. q_{max}. This means that the number of atoms in the surface layer is, $$N_s = \frac{1}{2\sqrt{3}(128\cdot10^{-12})^2} = 1.8\cdot 10^{19}$$, If you removed one electron per atom, you would have a surface charge of, $$\sigma = N \; e = 1.8\cdot 10^{19} \cdot 1.6\cdot 10^{-19} = 2.8\;\rm{C/m^2}$$. Why does the capacitor draw maximum current at the start of charging? Apr 2014 73 0 australia May 23, 2015 #1 here is the questions and the answers for them . Learn everything you need to know about capacitors, including capacitance, measuring electrical charge, and the different types of caps. Does French retain more Celtic words than English does? Also Read: Combination of Capacitors In an oscillating LC circuit the maximum charge on the capacitor is 2.2 C and the maximum current through the inductor is 7.5 mA. The relationship between surface charge density $\sigma$ of a capacitor with spacing $d$ is given by, Setting this equal to the Schwinger limit, we find the maximum surface charge, $$\sigma_{max}=2\epsilon_0 E_S = 2\cdot 8.85\cdot 10^{-12} \cdot 1.3 \cdot 10^{18} = 23 \;\rm{MC/m^2}$$, If the conductor is copper, the size of a copper atom is about 128 pm radius. The bitline's capacitance is much greater than that of the capacitor (approximately ten times). When the access transistor is activated, the electrical charge in the capacitor is shared with the bitline. There are capacitors that can hold 1 picofarad of charge (10-12 C) and there are other capacitors that can hold 4700F of charge. Does no correlation but dependence imply a symmetry in the joint variable space? @EmilioPisanty indeed you reach other limits first - I was just responding to the final paragraph of the question ("concern for atomic propertiesfixed number of charges"). The maximum charge capacitor can store On one plate is limited by which of the following How much charge can physically fit on the conclucting plales (B) The maximum time rale of change ol the charge on the other plate The nonzero energy needed t0 remove an electron from the conducting plates The finite value of the capacitance The electrical discharge when the electric field between the . Instead, I believe the best and simplest approach to solve these two questions a and b is Thevenin's theorem. Capacitor Charge Calculation. Since the voltage across the capacitor approaches the voltage across the terminals the electric field in the wires approaches zero and so the current approaches zero. In a dielectric breakdown, some of the (few) free charges in the dielectric are released by the electric field if it becomes too strong, and as they travel through the dielectric they ionize other parts of the material, setting up an avalanche reaction. Use MathJax to format equations. In an oscillating LC circuit the maximum charge on the capacitor is Q. The charge will approach a maximum value Q max = C. It is trivially the time it take for the capacitor to reach 63.2% of the . 2. As the capacitor is therefore fully charged no more charging current flows in the circuit so, The tolerance value is the extent to which the actual capacitance is allowed to vary from its nominal value and can range anywhere from. In this case, ensure that the charging voltage exceeds 90% of the capacitor voltage rating. The current is a maximum when the charge on the capacitor, how do other animals obtain the nitrogen they need. Stack Overflow for Teams is moving to its own domain! It supports a wide range of input and output measurement units. JavaScript is disabled. 2003-2022 Chegg Inc. All rights reserved. Meas. To find the maximum current. Capacitors do not store charge. What is the maximum charge on the capacitor LC circuit? A maximum specific capacitance of 238 F g(-1) is observed at a scan rate of 20 mV s(-1) . When the electric field magnitude in the capacitor is. (BEDO DRAM), could process four memory addresses in one burst, for a maximum of 5111, saving an additional three clocks over . Time constant of a CR circuit is thus also the time during which the charge on the capacitor falls from its maximum value to 0.368 (approx 1/3) of its maximum value. Therefore no more charge will flow to or from the plates of the capacitor. The maximum-charge limits on actual physical capacitors are dictated by the dielectric breakdown of the medium between the plates, which typically is an insulating dielectric of some kind - common materials are paper, plastic, glass, mica and ceramics, as well as air and vacuum. You have to account for the continually changing charge being applied to the capacitor. We know that the energy stored in the inductor . Transcribed image text: In an oscillating LC circuit, the maximum charge on the capacitor is 9.0 x 107 C and the maximum current through the inductor is 7.5 mA. Everything You Need to Know About Capacitors (2022 Update) Edwin Robledo November 4, 2022 11 min read. Can a trans man get an abortion in Texas where a woman can't? What is the maximum current through the inductor? If we assume that "one electron per atom missing" is an upper bound, this would correspond to a field of $159 \;rm{GV/m}$ - still a ridiculously high value, well above what can be maintained. These online calculators computes various parameters for charging and discharging the capacitor with the resistor. Youll find max voltages anywhere from 1.5V to 100V. Dielectrics in capacitors serve three purposes: to keep the conducting plates from coming in contact, allowing for smaller plate separations and therefore higher capacitances; to increase the effective capacitance by reducing the electric field strength, which means you get the same charge at a lower voltage; and. When do you need to make an Strength (Athletics) check to climb when you have a climb speed? Calculate the resistance from the average power and the rms voltage using equation 21-6. How can I make combination weapons widespread in my world? Maximum energy stored in capacitor,=12(Qmax)2CMaximum energy stored in Inductance=12L(Imax)2According to question,12(Qmax)2C=12L(Imax)2LC=(Qmax. N.M. Zimmerman. This mechanism is what makes cathode rays work, but at low temperature it's still present but at much lower intensity. Calculate the resistance from the average power and the rms voltage using equation 21-6. Maximum value of ultracapacitors made is 100,000 Farads. The maximum charge a capacitor stores depends on the voltage V 0 you've used to charge it according to the formula: Q 0 = C V 0 However, a real capacitor will only work for voltages up to the breakdown voltage of the dielectric medium in the capacitor. If the resistor was just 1000 ohms, the time constant would be 0.1seconds, so it would take 0.5 seconds to reach 9 volts. Aluminum-electrolytic capacitors such as the EPCOS B43504 or B43505in voltage ratings from 40 to 450 Vdc and capacitance values from 220 to 150 000 Fare typically used. High-Frequency, Regulated,200mA, Inverting Charge Pump2_____ABSOLUTE MAXIMUM RATINGSELECTRICAL CHARACTERISTICS(VIN = V SHDN = +5V, capacitors from Table 1, TA = 0C to +85C, unless otherwise noted. Certain types of caps have pulse ratings. The amount of charge Q a capacitor can store depends on two major factorsthe voltage applied and the capacitors physical characteristics such as its size. There are about 7 orders of magnitude between these: in other words, you will never be able to create a material that maintains its mechanical integrity and generates a field even close to the Schwinger limit. The charge will approach a maximum value Qmax = C. The total amount of charge on both the plates taken together is zero! The charging of a capacitor can be understood as follows . Experts are tested by Chegg as specialists in their subject area. Based on the pulsed electroacoustic method, the traditional circuit design under highfrequency voltages is first analysed. How do you find the maximum current in a RLC circuit? 45 no. How do you find the maximum charge of a capacitor? Our NPC is very promising for efficient electrodes for high-performance supercapacitor applications. So the amount that a capacitor can charge depends on the capacitor at hand. If one plate of a capacitor has 1 coulomb of charge stored on it the other plate will have 1 coulomb making the total charge (added up across both plates). The Capacitor Charge/Charging Calculator calculates the voltage that a capacitor with a capacitance, of C, and a resistor, R, in series with it, will charge to after time, t, has elapsed. Thus, the capacitor acts as a source of . Capacitors come in a whole range of capacitance capabilities. Taking issue with your opening paragraph: since one electrode gets excess electrons (from an external, infinite supply) and the other gets electrons taken away (finite supply), I would say there. When the voltage source has a step function it is at the start. The charging current is = I max = A. What is the total charge on each plate given that the area of the plates is 10cm by 10cm? Typical values are at TA = +25C. (especially in a vacuum) And you will no longer have a "capacitor plate" but a gas of mutually/electrostatically-repulsive particles Or alternatively, heat the cathodes a lot to produce diodes and tube -amplifiers! The voltage on the capacitor changes as it charges or discharges. What is the total charge on each plate given that the area of the plates is 10cm by 10cm? Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. When the current in the inductor is maximum which is true about the charge in the capacitor? 10. When all the energy is in the capacitor it will have maximum charge. Take the . Inputs Supply voltage V Capacitance F Series Resistance Outputs Energy: Joules Time Constant: seconds Calculating Energy Stored in a Capacitor Instrum. Part (b) What is the time interval, in seconds, between an instant when the capacitor is uncharged and the next instant when it is fully charged. How do you find the charge of a capacitor in series? By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. In air, the dielectric breakdown mode is simply avalanche sparking between the plates. When the voltage source has a step function it is at the start. For b) I have a feeling Qmax for the capacitor will be Qmax = CV where V is the voltage across R2 since R2 and C are parallel, but I can't figure out V across R2 in terms of E, R1, R2, C. The above approach involves some mathematical calculations and a generalized expression for current I(t). As the capacitor charges the voltage across the resistor drops ( V R = V V cap) so the current through it drops. Otherwise it will explode! You can use this calculator to calculate the voltage that the capacitor will have charged to after a time period, of t, has elapsed. The time constant, = RC = 1, the maximum voltage of battery, Vs = 10 volt and the time, t = 2 second. [2] Correct answers: 2 question: In an oscillating LC circuit, when 86.6% of the total energy is stored in the inductor's magnetic field, (a) what multiple of the maximum charge is on the capacitor and (b) what multiple of the maximum current is in the inductor Electric field lines in this parallel plate capacitor as always start on positive charges and end on negative charges. A parallel plate capacitor has a capacitance of 2 micro-farads. A graph of the charge on the capacitor versus time is shown in Figure \(\PageIndex{2a}\) . What is the maximum charge on the capacitor? Audioguru. If one plate of a capacitor has 1 coulomb of charge stored on it the other plate will have 1 coulomb making the total charge (added up across both plates) zero. How do you find the maximum current in a LC circuit? 5, 841 (1996); NIST eprint. Would drinking normal saline help with hydration? When a discharged capacitor is suddenly connected across a DC supply, such as Esin figure 1 (a), a current immediately begins to flow. It is zero. At a given instant later. . An AC circuit experiences 100% voltage reversal, while underdamped DC circuits experience less than 100%. Texas Instruments show that the typical output current of a CD4047 with a 10V supply is 10mA into a short circuit when the capacitor is beginning to charge and is 7.5mA when the capacitor is charged to half the supply voltage. Youll find max voltages anywhere from. What is the capacitance of this capacitor? and the charge on the capacitor is = Qmax = C. Different capacitors have different charge capacities. Otherwise it will explode! close. In an oscillating LC circuit the maximum charge on the capacitor is Q. This time span is called the charging time of the capacitor. C = F RC = s = time constant. The capacitance of a capacitor can be defined as the ratio of the amount of maximum charge (Q) that a capacitor can store, If I1 is the smallest current then the currents through the parallel resistors are guaranteed to be smaller than their maximums.
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