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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