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Lecture 2:Circuit Elements and Series/Parallel ResistorsNilsson 2.1-2.5, 3.1-3.2

ENG17 (Sec. 1): Circuits I

Summer 1 2014

June 24, 2014

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Overview

• Voltage & Current Sources

• Electrical Resistance• Circuit Model• Kirchhoff’s Laws• Dependent Sources• Series / Parallel

Resistors

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5 Ideal Basic Circuit Elements

• Voltage Sources• Current Sources• Resistors• Inductors• Capacitors

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Ideal SourcesVoltage Source(const. voltage)

Current Source(const. current)

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Dependent Sources

Voltage Sources Current Sources

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Schematics

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Schematics (w/dependents)

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Schematics - GND

• Ground (GND) is a common connection• Typically connect to Earth GND• Always a zero [V] reference potential

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Overview

• Voltage & Current Sources

• Electrical Resistance• Circuit Model• Kirchhoff’s Laws• Dependent Sources• Series / Parallel

Resistors

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Ohm’s Law

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Conductance

• Conductance, G– Units: siemens [S]

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Power & Ohm’s Law

𝑉=𝐼𝑅

𝑃= 𝐼𝑉

Therefore…

Ohm’s Law

Power Relationship

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Examples

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Overview

• Voltage & Current Sources

• Electrical Resistance• Circuit Model• Kirchhoff’s Laws• Dependent Sources

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Designing a Circuit Model

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Additional Elements

Short Circuit

Open Circuit

Switch

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Schematic

1.5V 9V

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Overview

• Voltage & Current Sources

• Electrical Resistance• Circuit Model• Kirchhoff’s Laws• Dependent Sources• Series / Parallel

Resistors

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The Setup

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Kirchhoff’s Current Law (KCL)

The algebraic sum of all the currents at any node in a circuit equals zero.

Therefore:• Assign signs to currents at each node• Positive (+) for current leaving a node• Negative (-) for current entering a node• Or vice versa

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Kirchhoff’s Voltage Law (KVL)

The algebraic sum of all the voltages around any closed path in a circuit equals zero.

Therefore:• Assign signs to voltages in a loop• Positive (+) for voltage rise• Negative (-) for voltage drop• Or vice versa

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Observations

• 7 equations 4 equations– Because I and V are related

through R, we only need one

• With only 2 branches at a node (in series), we only need to know 1 current

𝑣1=𝑖1𝑅1

𝑣𝑐=𝑖𝑐𝑅𝑐

𝑣 𝑙=𝑖𝑙𝑅 𝑙

𝑖𝑠− 𝑖1=0𝑖1+𝑖𝑐=0−𝑖𝑐−𝑖𝑙=0𝑖𝑙−𝑖𝑠=0

𝑣 𝑙−𝑣𝑐+𝑣1−𝑣𝑠=0

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KCL Example

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KVL Example

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Overview

• Voltage & Current Sources

• Electrical Resistance• Circuit Model• Kirchhoff’s Laws• Dependent Sources• Series / Parallel

Resistors

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Finding vo

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Finding vo

KVL:

KCL:

Ohm’s Law:

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Overview

• Voltage & Current Sources

• Electrical Resistance• Circuit Model• Kirchhoff’s Laws• Dependent Sources• Series / Parallel

Resistors

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Series Connected Elements

• Resistors in series carry the same current– KCL proves this

• Resistors in series can be summed– KVL proves this

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Parallel Connected Elements

• Resistors in parallel have same voltage across their terminals– KVL proves this

• Resistors in parallel can be summed inversely– KCL proves this– Conductances are summed

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Example

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Recap

• Voltage & Current Sources

• Electrical Resistance• Circuit Model• Kirchhoff’s Laws• Dependent Sources• Series / Parallel

Resistors