ESE 271 / Spring 2013 / Lecture 2
Last time we learned
Passive sign convention
Circuit element absorbs power – acts lik l d
like a load
Circuit element delivers power – acts like a generator
Energy delivered to circuit element by time t
Passive circuit elements:
Active circuit elements:
Example of active circuit elements: ideal independent voltage and current sources
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ESE 271 / Spring 2013 / Lecture 2
Last time we discussed
Example
We will be working with lumped‐parameter model circuits (energy is lumped within circuit elements)
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ESE 271 / Spring 2013 / Lecture 2
Kirchhoff’s Current Law (KCL)
Node can not accumulate any charge, hence current entering the node should be equal to the current leaving the node.
Example Example
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ESE 271 / Spring 2013 / Lecture 2
Kirchhoff’s Voltage Law (KVL)
Sum of voltage drops around any closed loop is zero.
Example Sum of voltage drops = Sum of voltage rises
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ESE 271 / Spring 2013 / Lecture 2
Example
KCL at node A
KCL at node B
KCL at node B
KVL around loop
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ESE 271 / Spring 2013 / Lecture 2
Current in circuit element
Let’s find the velocity of electrons moving in constant electric field
‐ Newton’s equation of motion
It follows from this analysis that the velocity of electrons f
f
y
y f
and, hence, electric current should increase in time when voltage drop (i.e. electric field) remains constant.
This conclusion is not supported by experiment.
pp
y p
What is wrong in our analysis?
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ESE 271 / Spring 2013 / Lecture 2
Ohm’s Law
Drift velocity
Average time between collisions
Drift current density:
if
d i
Conductance
Conductivity
Drift current:
Ohm’s law:
‐ Resistance
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ESE 271 / Spring 2013 / Lecture 2
Resistor
Resistivity
Passive sign convention
Power delivered to resistor:
Energy delivered to ideal resistor is being dissipated immediately and gets converted into heat. No energy is stored.
(collision of moving electrons with imperfections is friction)
(collision of moving electrons with imperfections is friction)
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ESE 271 / Spring 2013 / Lecture 2
Example
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ESE 271 / Spring 2013 / Lecture 2
Power rating
Real resistors can not dissipate more than certain amount of power without additional heatsink.
The power rating limits the maximum values of the current that can be sent through the resistor and maximum value of the voltage that can be applied.
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ESE 271 / Spring 2013 / Lecture 2
Series connection of resistors
KVL:
KCL: current is the same in all elements
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ESE 271 / Spring 2013 / Lecture 2
Voltage divider
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ESE 271 / Spring 2013 / Lecture 2
Example
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ESE 271 / Spring 2013 / Lecture 2
Series connection of voltage sources
KVL:
Equivalent voltage
source
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ESE 271 / Spring 2013 / Lecture 2
Series connection of ideal current sources
What values of
are physically possible?
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ESE 271 / Spring 2013 / Lecture 2
Example
KCL:
KVL:
KCL:
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ESE 271 / Spring 2013 / Lecture 2
Parallel connection of resistors
KCL at node 1:
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ESE 271 / Spring 2013 / Lecture 2
Current divider
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ESE 271 / Spring 2013 / Lecture 2
Parallel connection of current sources
KCL:
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ESE 271 / Spring 2013 / Lecture 2
Parallel connection of ideal voltage sources
What values of
are p
physically
y
yp
possible?
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ESE 271 / Spring 2013 / Lecture 2
Example
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ESE 271 / Spring 2013 / Lecture 2
Equivalent subcircuits
This is equivalent two‐terminal subcircuit.
Thi
i
i l
i l b i i
Equivalent means it has the same terminal voltage and current.
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ESE 271 / Spring 2013 / Lecture 2
Equivalent subcircuits – another example
This is equivalent This
is equivalent
two‐terminal subcircuit.
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