ESE 271 / Spring 2013 / Lecture 2

Last time we learned

Passive sign convention Circuit element absorbs power –acts like a lldoad

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 and current sources

1 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)

2 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

3 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

4 ESE 271 / Spring 2013 / Lecture 2

Example

KCL at node A

KCL at node B

KVL around loop

5 ESE 271 / Spring 2013 / Lecture 2

Current in circuit element

Let’s find the velocity of electrons moving in constant ‐ Newton’s equation of motion

It follows from this analysis that the velocity of electrons and, hence, should increase in time when voltage drop (i.e. electric field) remains constant.

This conclusion is not supported by experiment.

What is wrong in our analysis? 6 ESE 271 / Spring 2013 / Lecture 2

Ohm’s Law

Drift velocity Average time between collisions

Drift current ddiensity: Conductance Conductivity

Drift current:

Ohm’s law: ‐ Resistance

7 ESE 271 / Spring 2013 / Lecture 2

Resistor

Resistivity

Passive sign convention

Power delivered to :

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)

8 ESE 271 / Spring 2013 / Lecture 2

Example

9 ESE 271 / Spring 2013 / Lecture 2

Power rating

Real 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.

10 ESE 271 / Spring 2013 / Lecture 2

Series connection of resistors

KVL:

KCL: current is the same in all elements

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Voltage divider

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Example

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Series connection of voltage sources

KVL:

Equivalent voltage source

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Series connection of ideal current sources

What values of

are physically possible?

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Example

KCL:

KVL:

KCL:

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Parallel connection of resistors

KCL at node 1:

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Current divider

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Parallel connection of current sources

KCL:

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Parallel connection of ideal voltage sources

What values of

are ppyhysically yp possible?

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Example

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Equivalent subcircuits

This is equilivalent two‐termilinal subibcircu it. Equivalent means it has the same terminal voltage and current.

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Equivalent subcircuits –another example

This is equivalent two‐terminal subcircuit.

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