Notes - Week of September 24th

Notes - Week of September 24th - Class notes for the week...

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Class notes for the week of September 24 th 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 . 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: ( 29 2 1 2 1 0 2 1 R R I V R I R I V R I R I V + = - = = - - 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 10kohm (8k for R1 plus 2k for R2 ). We define the equivalent resistance, R eq , of the series connected R1 and R2 as: 2 1 R R R eq + = 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: = n n eq R R 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 2Vdc reference and you have only a 5Vdc power on your board. The voltage divider is just two resistors connected in series as shown below: I R 1 8 k R 2 2 k R 3 6 . 8 k R 4 3 . 6 k R 5 7 . 2 k R 6 4 . 2 k R 1 8 7 . 2 k R 1 9 7 . 2 k

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The output voltage, Vout , is taken across R2 . Technically, this is not a series circuit since we have a
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Notes - Week of September 24th - Class notes for the week...

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