EE 221 Review 1 Basic components Electric circuits Voltage and current laws

Basics - SI base units Base quantityNameSymbol lengthmeterm masskilogramkg timeseconds electric currentampereA temperaturekelvinK

Basics - SI prefixes FactorNameSymbolFactorNameSymbol attoa femtof picop10 12 teraT nanon10 9 gigaG micro  10 6 megaM millim10 3 kilok centic

Basics - Charge Two types of charge –positive: (proton) –negative: (electron, C) Continuously transferring charge –total amount of charge never changed –neither created nor destroyed (conservation) Defined in terms of ampere Measured in coulomb (C) = As

Basics - Current Charge in motion –transfer of energy –related to charge Representing current –numerical value (+ unit) (e.g., A) –direction ( ) –unit is the ampere (A) –represented by I, i, i(t) Symbol for an independent current source

Basics - Current Example (a,b) Incomplete, improper, and incorrect definitions of a current. (c) the correct definition of i 1 (t).

General, simple circuit element –two terminals –cannot be decomposed further –completely characterized by its voltage-current relationship Pushing charge –expenditure of energy –electrical voltage (potential difference) –voltage "across" the element Basics - Voltage A general two-terminal circuit element

Voltage measures work required to move charge Representing voltage –numerical value (+ unit) (e.g., -2.5 V) –direction (sense) ( + V - ) (left terminal is V volts positive with respect to the right terminal) –unit is volt (V = J / C) –represented by V, v, v(t) Basics - Voltage A general two-terminal circuit element Symbols: (a) DC voltage source; (b) battery; (c) ac voltage source.

Power is the rate of energy expenditure: Voltage * Current –Voltage defined in terms of energy –Current is rate at which charge moves Representing power – numerical value (+ unit) (e.g., -5.6 W) – "direction" by Passive Sign Convention – PSC: Current entering element through positive terminal – unit is watt (W = V *A = J / C *A = J / (As) *A = J / s) – represented by P, p, p(t) Basics - Power A general two-terminal circuit element

Is a choice we make (convention) The current arrow is directed into the "+" marked terminal The power absorbed by the element is given by the product p = v i A negative value indicates that power is actually generated Or: The power generated by the element is given by the product p = - v i Basics - Passive sign convention ( PSC) A general two-terminal circuit element, p = vi represents the power absorbed

Resistance of conducting element Ohm's law: v = R i –linear, directly proportional Passive element Power p = v i = i 2 R = v 2 / R Representing resistance –numerical value (+ unit) (e.g., 3  ) –unit is ohm (  = V / A) –represented by R Basics - Resistor

Nodes Branches Paths Loops Circuits (a) A circuit containing three nodes and five branches. (b) Node 1 is redrawn to look like two nodes; it is still one node.

Kirchhoff's current law Conservation of charge Circuits - KCL The algebraic sum of the currents entering any node is zero. i A + i B - i C - i D = 0

Kirchhoff's voltage law Conservation of energy Circuits - KVL The algebraic sum of the voltages around any closed path is zero. v 1 = v 2 - v 3

Circuits - Sources (a) Series connected voltage sources can be replaced by a single source. (b) Parallel current sources can be replaced by a single source.

Circuits - Sources Examples of circuits with multiple sources, some of which are “illegal” as they violate Kirchhoff’s laws.

V-I Laws: Resistors (a) Series combination of N resistors. (b) Electrically equivalent circuit. R eq = R 1 + R R N

V-I Laws: Resistors (a) Parallel combination of N resistors. (b) Electrically equivalent circuit. 1/R eq = 1/R 1 + 1/R /R N A special case worth remembering is

Voltage division Using KVL and Ohm's law to find v 2. An illustration of voltage division. For a string of N series resistors....

Current division Using KCL and Ohm's law to find i 2. For a parallel combination of N resistors the current through R k equals.... An illustration of current division.

Simplifying circuits (KVL) V 1 = V a - V b + V c V 2 = -V a + V b - V c What do we count as positive? Direction of summation determines polarity 1st choice 2nd choice