notes%204 - Class notes #4 Series connected resistors If...

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Class notes #4 Series connected resistors If two components are connected ‘end-to-end’, and there are no other components connected to their junction, then the components are said to be connected in series. In the example at right resistors R18 and R5 are in series, but R4 and R6 are not in series since there is another component connected to their junction. The important thing about series connected components is that the current through both components is the same. This permits some simplifications to be made. Consider the circuit shown at left. R1 and R2 are in series, and they must carry the same current, I . Ohm’s law tells us that the voltage across R1 is I*R1 with the positive sign on top, while the voltage across R2 is I*R2 also with the positive sign toward the top of the page. If we write a KVL equation around the loop we obtain: This has the same form as Ohm’s law, except that the resistance, R, has been replaced with R1+R2. It appears that the circuit works exactly the same as if there were a single resistor of value 10 kohm (8 k for R1 plus 2 k for R2 ). We define the equivalent resistance, R eq , of the series connected R1 and R2 as: It is easy to extend this idea to any number of resistors in series, so that the equivalent resistance of n resistors in series is just the sum of the resistances of all n resistors: Voltage divider An especially handy series resistor circuit is the voltage divider. Its use is to produce a scaled (or divided) voltage output from a higher voltage. You might use a resistor divider if you need a 2 Vdc voltage reference and you have only 5 Vdc power in your circuit. A voltage divider is just two resistors connected in series as shown below:
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This note was uploaded on 10/21/2010 for the course ESE 123 taught by Professor Westerfield during the Fall '07 term at SUNY Stony Brook.

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notes%204 - Class notes #4 Series connected resistors If...

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