15 Kirchoff's Laws


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Unformatted text preview: tors for reasonable values of V and I. We also define the “conductance” G = 1/R with units of Siemens (s). In older times in the U.S. the unit mho was used. This is not done any more. 15.8 You should also notice that Ohm’s law applies for the time varying case as well, i.e. It is also important to understand that a resistor is a passive element that always consumes power. This power is turned into heat due to the collisions we described below. Thus when the passive sign convention is used, the power P = VI is always positive. You should also notice that for a resistor we have: P = V I = (I R) I = I2 R or P VI V V V2 RR which do also apply in the time‐varying case: p(t ) v(t )i(t ) i(t )R i(t ) i 2 (t )R or p(t ) v(t )i(t ) v(t ) v(t ) v 2 (t ) R R Examples [DeCarlo/Lin p. 27] P V 2 144 18W R 8 P I2R 16 10 160W Example (Alan 1.27) 15.9 i) I = ?? ii) Pr ?? iii) Ps ?? Ans: i) The voltage drop across the resistor equals the voltage supplied by the source (parallel connection). V 6 Thus V0 6V and by Ohm’s law: I 0 I 12 A . Notice that this is also the current R 0.5 supplied by the source. ii) The power consumed by the resistor is: PR V0I (notice that the direction of I is from positive to negative voltage). Thus: PR (6V ) (12 A) 72W Also notice that the same answer can be obtained from the other formulas for power in conjunction with Ohm’s law: 72 W General equation Only for resistors iii) Due to conservation of power the power supplied by the source has to be equal to the power consum...
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This note was uploaded on 03/06/2014 for the course ECE 201 taught by Professor All during the Spring '08 term at Purdue.

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