By John O'Malley

ISBN-10: 0070478244

ISBN-13: 9780070478244

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**Extra resources for Schaum s outline of theory and problems of basic circuit analysis**

**Example text**

KIRCHHOFF’S CURRENT LAW AND PARALLEL DC CIRCUITS Kirchhofi’s current k m ~ abbreviated , KCL, has three equivalent versions: At any instant in a circuit, 1. The algebraic sum of the currents leaving a closed surface is zero. 2. The algebraic sum of the currents entering a closed surface is zero. 3. The algebraic sum of the currents entering a closed surface equals the algebraic sum of those leaving. The word “algebraic” means that the signs of the currents are included in the additions. Remember that a current entering is a negative current leaving, and that a current leaving is a negative current entering.

The expression reduces to 12116, which is (12 x 6)/(12 + 6) = 4. Thus, R,. = 4 R. 4 1 Find the total resistance R , of the resistor ladder network shown in Fig. 3-19. To find the equivalent resistance of a ladder network by combining resistances, always start at the end opposite the input terminals. At this end, the series 4- and 8-R resistors have an equivalent resistance of 12 R. This combines in parallel with the 24-R resistance: (24 x 12)/(24+ 12) = 8 R. This adds to the 3 and the 9 R of the series resistors for a sum of 8 + 3 + 9 = 20 R.

Then from R , = 1 # G,. ), + + + R,. = 1 I/R, + 1/R2 + 1/R, + * * An important check on calculations with this formula is that R , must always be less than the least resistance of the parallel resistors. For the special case of just two parallel resistors, So, the total or equivalent resistance of two parallel resistors is the product of the resistances divided by the sum. The symbol 11 as in R,IIR, indicates the resistance of two parallel resistors: R I IiR, = R , R 2 ( R , + R 2 ) . It is also sometimes used to indicate that two resistors are in parallel.

### Schaum s outline of theory and problems of basic circuit analysis by John O'Malley

by John

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