Lecture 2: Circuit Elements and Series/Parallel Resistors Nilsson , ENG17 (Sec. 1): Circuits I Summer June 24, 2014

Overview Voltage & Current Sources Electrical Resistance Circuit Model Kirchhoff’s Laws Dependent Sources Series / Parallel Resistors 2

5 Ideal Basic Circuit Elements Voltage Sources Current Sources Resistors Inductors Capacitors 3

Ideal Sources 4 Voltage Source (const. voltage) Current Source (const. current)

Dependent Sources 5 Voltage Sources Current Sources

Schematics 6

Schematics (w/dependents) 7

Schematics - GND Ground (GND) is a common connection Typically connect to Earth GND Always a zero [V] reference potential 8

Overview Voltage & Current Sources Electrical Resistance Circuit Model Kirchhoff’s Laws Dependent Sources Series / Parallel Resistors 9

Ohm’s Law 10

Conductance 11

Power & Ohm’s Law 12 Therefore… Ohm’s Law Power Relationship

Examples 13

Overview Voltage & Current Sources Electrical Resistance Circuit Model Kirchhoff’s Laws Dependent Sources 14

Designing a Circuit Model 15

Additional Elements 16 Short Circuit Open Circuit Switch

Schematic V9V

Overview Voltage & Current Sources Electrical Resistance Circuit Model Kirchhoff’s Laws Dependent Sources Series / Parallel Resistors 18

The Setup 19

Kirchhoff’s Current Law (KCL) 20 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

Kirchhoff’s Voltage Law (KVL) 21 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

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 22

KCL Example 23

KVL Example 24

Overview Voltage & Current Sources Electrical Resistance Circuit Model Kirchhoff’s Laws Dependent Sources Series / Parallel Resistors 25

Finding v o 26

Finding v o 27 KVL: KCL: Ohm’s Law:

Overview Voltage & Current Sources Electrical Resistance Circuit Model Kirchhoff’s Laws Dependent Sources Series / Parallel Resistors 28

Series Connected Elements Resistors in series carry the same current –KCL proves this Resistors in series can be summed –KVL proves this 29

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 30

Example 31

Recap Voltage & Current Sources Electrical Resistance Circuit Model Kirchhoff’s Laws Dependent Sources Series / Parallel Resistors 32