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When you lift a book, you increase its gravitational potential energy This can be interpreted as storing energy in a gravitational field In a similar way, you can store energy in an electric field In 1746, Dutch physician and physicist Pieter Van Musschenbroek invented a small device that could store a large electric charge In honor of the city in which he worked, it was called a Leyden jar Benjamin Franklin used a Leyden jar to store the charge from lightning and in many other experiments A version of the Leyden jar is still in use today in electric equipment This new device for storing a charge has a new form, is much smaller in size, and is called a capacitor As charge is added to an object, the electric potential difference between that object and Earth increases For a given shape and size of an object, the ratio of charge stored to electric potential difference, q/ V, is a constant called the capacitance, C For a small sphere far from the ground, even a small amount of added charge will increase the electric potential difference Thus, C is small A larger sphere can hold more charge for the same increase in electric potential difference, and its capacitance is larger Capacitors are designed to have specific capacitances All capacitors are made up of two conductors that are separated by an insulator The two conductors have equal and opposite charges Capacitors are used today in electric circuits to store charge Commercial capacitors, such as those shown in Figure 21-14, typically contain strips of aluminum foil separated by thin plastic that are tightly rolled up to conserve space The capacitance of a capacitor is independent of the charge on it, and can be measured by first placing charge q on one plate and charge q on the other, and then measuring the electric potential difference, V, that results The capacitance is found by using the following equation, and is measured in farads, F Capacitance C.

The farad as a unit of measure One farad, F, named after Michael Faraday, is one coulomb per volt, C/V Just as 1 C is a large amount of charge, 1 F is also a fairly large capacitance Most capacitors used in modern electronics have capacitances between 10 picofarads (10 10 12 F) and 500 microfarads (500 10 6 F) However, memory capacitors that are used to prevent loss of memory in some computers can have capacitance from 05 F to 10 F Note that if the charge is increased, the electric potential difference also increases The capacitance depends only on the construction of the capacitor, not on the charge, q

Finding Capacitance A sphere has an electric potential difference between it and Earth of 400 V when it has been charged to 24 10 6 C What is its capacitance

24 10

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Multidimensional arrays have more than one dimension: int[,] matrix = new int[4, 2]; matrix[0, 0] = 5; matrix[3, 1] = 10; The matrix array has a first dimension of 4 and a second dimension of 2. This array could be initialized using the following statement: int[,] matrix = { {1, 1}, {2, 2}, {3, 5}, {4, 5}}; The matrix array has a first dimension of 5 and a second dimension of 2. Multidimensional arrays are sometimes called rectangular arrays because the elements can be written in a rectangular table (for dimensions less than 2). When the matrix array is allocated, a single chunk is obtained from the heap to store the entire array (see Figure 16-1).

Draw a sphere above Earth and label the charge and potential difference Known:

%00001111

400 V

Unknown:

24 10

Are the units correct C/V = F The units are farads Is the magnitude realistic A small capacitance would store a small charge at a low voltage

Figure 16-1. Storage in a multidimensional array The following is an example of using a multidimensional array: using System; class Test { public static void Main() { int[,] matrix = { {1, 1}, {2, 2}, {3, 5}, {4, 5}, {134, 44} }; for (int i = 0; i < matrix.GetLength(0); i++) { for (int j = 0; j < matrix.GetLength(1); j++) { Console.WriteLine("matrix[{0}, {1}] = {2}", i, j, matrix[i, j]); } } } }

30 A 27- F capacitor has an electric potential difference of 45 V across it What is the charge on the capacitor 31 Both a 33- F and a 68- F capacitor are connected across a 24-V electric potential difference Which capacitor has a greater charge What is it 32 The same two capacitors as in problem 31 are each charged to 35 10 the larger electric potential difference across it What is it

33 A 22- F capacitor first is charged so that the electric potential difference is 60 V How much additional charge is needed to increase the electric potential difference to 150 V 34 When a charge of 25 10 5 C is added to a capacitor, the potential difference increases from 120 V to 145 V What is the capacitance of the capacitor

pullup %00011110

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