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Notice that in each case the conservation of energy is satis ed; that is, the sum of the voltages across R2 and R4 and the sum of the voltages across R1 and R3 are equal to the value of the voltage source V2 + V4 = 5 + 10 = 15 V V1 + V3 = 375 + 1125 = 15 V Now we know the voltage across every resistor in Fig 3-19 and can nd the Thevenin equivalent voltage by taking any loop we like and applying KVL Taking the top loop around VTH , R1 , and R2 we have VTH V1 + V2 = 0 VTH = V2 V1 = 5 375 = 125 V Let s nd the Thevenin equivalent resistance First we set the voltage source equal to zero and replace it by a short circuit Then we have the circuit shown in Fig 3-21 The combinations R1 R3 and R2 R4 are in parallel So the circuit shown in Fig 3-21 is equivalent to the circuit shown in Fig 3-22

The mapping of objects to les is in many ways like the mapping of tuples to les in a relational system At the lowest level of data representation, both tuples and the data parts of objects are simply sequences of bytes We can therefore store object data in the le structures described in this chapter, with some modi cations which we note next Objects in object-oriented databases may lack the uniformity of tuples in relational databases For example, elds of records may be sets; in relational databases, in con-

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The McGraw Hill Companies, 2001

trast, data are typically required to be (at least) in rst normal form Furthermore, objects may be extremely large Such objects have to be managed differently from records in a relational system We can implement set-valued elds that have a small number of elements using data structures such as linked lists Set-valued elds that have a larger number of elements can be implemented as relations in the database Set-valued elds of objects can also be eliminated at the storage level by normalization: A relation is created containing one tuple for each value of a set-valued eld of an object Each tuple also contains the object identi er of the object However, this relation is not made visible to the upper levels of the database system The storage system gives the upper levels of the database system the view of a set-valued eld, even though the set-valued eld has actually been normalized by creating a new relation Some applications include extremely large objects that are not easily decomposed into smaller components Such large objects may each be stored in a separate le We discuss this idea further in Section 1196

Fig 3-21 The circuit used to nd the equivalent resistance for Example 3-5

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