Lecture 2

•Review Passive Sign Convention•Power Generation, Absorption•Power Sources•Resistance•Related educational modules:

–Sections 1.1, 1.2, 1.3

Passive sign convention – review• Passive sign convention:

• For passive circuit elements, we assume that the current enters the node with the higher voltage potential

• Your analyses will not be reliable unless you do this correctly

• Examples:

Subscript notation can denote voltage polarity• Voltage polarity is sometimes indicated by subscript

notation• The order of the subscripts indicates the polarity

• The first subscript indicates assumed higher-voltage node• The second subscript is the assumed lower-voltage node

Note:

vBA = -vAB

“Ground”• Voltages are often represented as relative to

“ground”:• Ground (symbol: ) is a reference voltage; often 0V• Voltages relative to ground generally not called a voltage

difference; they are a difference relative to zero volts• Voltages relative to ground often represented with a single

subscript

Power Generation and Dissipation

• Circuit elements can either dissipate or generate power

• Power is dissipated (or absorbed) if current enters the positive voltage node

–

• Power is generated (or supplied) if current enters the negative voltage node

Power Generation and Dissipation• Power = voltagecurrent (p= vi)

• Power is absorbed if the power is positive (voltage and current are consistent with the passive sign convention)

• Power is generated if the power is negative (voltage and current not consistent with the passive sign convention)

6W absorbed 6W generated

Examples

• Determine the power absorbed by the circuit element below.

• The circuit element absorbs 10W. Determine the current in the element.

Power Supplies

• Power supplies provide a source of electrical power

• Conceptual types of power supplies (models of physical supplies):• Voltage, current sources• Independent, dependent sources• Ideal and non-ideal sources

Independent voltage sources• Common symbols:

• Independent voltage sources maintain specified voltage, regardless of the current

Independent voltage sources – continued

• Voltage-current characteristic for constant voltage source:

i

VS

Power generated when current is

negative

Power absorbed when current is

positive

Independent current sources

• Common symbol:

• Independent current sources maintain specified current, regardless of the voltage

Independent current sources – continued

• Voltage-current characteristic for constant current source:

IS

v

i

Power generated when voltage is

positive

Power absorbed when voltage is

negative

Ideal power sources – limitations

• Ideal sources can provide infinite power• Voltage sources provide specified voltage, regardless of

the current current can be infinite power can be infinite

• Current sources provide specified current, regardless of the voltage voltage can be infinite power can be infinite

• These models can be unrealistic• We will examine more realistic power source models

later

Dependent Power Supplies• Some active circuit elements can be modeled as

dependent power sources• The current or voltage delivered by the source is

controlled by a current or voltage somewhere else in the circuit

• Four possible combinations• Voltage controlled voltage source (VCVS)• Current controlled voltage source (CCVS)• Voltage controlled current source (VCCS)• Current controlled current source (CCCS)

Dependent Power Supplies – continued

• Examples:

Resistors• Circuit symbol:

• R is the resistance• Units are ohms ()

• Voltage-current relation (Ohm’s Law):

)t(iR)t(v

Resistors – continued

• Notes:• Resistors can only dissipate energy • The voltage-current relation is algebraic

Resistor Power Dissipation• Ohm’s Law:

• Power:

• Combining:

)t(iR)t(v R

)t(v)t(i

)t(i)t(v)t(p

R

)t(v)t(v)t(p

R

)t(v)t(p

2

)t(Ri)t(p 2)t(Ri)t(i)t(p

Example

• Determine the power (generated or absorbed) by the resistor below:

Conservation of energy

• In an electrical circuit, the power generated is the same as the power absorbed

• Slightly more mathematically,

• Recall that power absorbed is positive and power generated is negative

0elements All

p

Conservation of power – example• Determine the power (absorbed or generated) by the

voltage source VS