power_and_sign_convention - R. Hannemann Power and Sign...

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Unformatted text preview: R. Hannemann Power and Sign Convention - Learning Objectives - Be able to explain active and passive elements - Be able to find generated or dissipated power of elements - Be able to use correct element labeling - Be able to use the passive sign convention - Be able to use the concept of conservation of power 06/13/06 1 Power I Electric Power: Mechanics: Voltage=Work/Charge Current=Charge/Time Power=Work/Time 1%me q I Unit of Power' [ J - P]=VA=—= W (Watt) S 06/13/06 2 EE305 Summer 2006 R. Hannemann Power ll - Power is a signed quantity - elements generate power —> active elements ° elements dissipate power —> passive elements - Two ways to choose sign for generated/ dissipated power. Most Commonly: Passive Sign Convention: Dissipated power is counted positive and generated power is counted negative. 06/13/06 Conservation of Power In an electrical circuit, power is conserved: All power generated by active elements will be dissipated by the passive elements in the same circuit. N Z P :0 Conservation i of Power i = 1 06/13/06 EE305 Summer 2006 R. Hannemann Element Labeling - Labeling of current and voltage at an element does not have to coincide with actual directions of these quantities - You can compare element labeling to probe attachment of multimeters: the reading of the meter can be positive or negative - circuit analysis works the same way: the actual analysis shows a positive or negative value for the quantity depending on the chosen labeling 06/13/06 Element Labeling Sign Convention 1 l a % + + V _ W > 0 _ V Active Element Passive Element generates power dissipates power 06/13/06 EE305 Summer 2006 R. Hannemann Using the sign convention I For all practical applications, the passive or active nature of elements in a circuit to be analyzed is known. The following algorithm ensures consistency in power computations: 1 . Assign consistent currents to all circuit branches containing voltage sources. Consistent means that the current in that branch is assigned such that it flows out of the voltage source's positive terminal. Based on this, the voltage across each passive element is assigned such that the current enters its positive terminal. 06/13/06 Using the sign convention || 2. Assign consistent voltages to all circuit branches containing current sources. Consistent means again that the voltage across each passive element is assigned such that the current enters its positive terminal. 3. Assign consistent currents and voltages to all branches containing passive elements. Note that this includes a degree of freedom in that you get to choose either the direction of the voltage or the current initially. 06/13/06 EE305 Summer 2006 R. Hannemann Using the sign convention I” 4. Analyze the circuit to find the unknown voltages and currents. 5. Compute the product of voltage and current for each element. If the product is positive, the labeling of the element as passive or active is correct. This should always be the case for elements of which the classification is known a priori. 06/13/06 9 Using the sign convention IV 6. Apply the passive sign convention to check for conservation of power: i. For all passive elements, the power is p=vi and thus dissipated by the element. ii. For all active elements, the power is p=-vi and thus generated by the element. 06/13/06 10 EE305 Summer 2006 ...
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