Introduction COURSE OBJECTIVE: To develop a set of principles and techniques for predicting circuit behavior Circuit – an interconnection of electrical elements, and “manipulates” electrical energy (generation, amplification, modulation, detection, conversion, etc.). Behavior – current and voltage are the variables of interest.

SYSTEMS OF UNITS: Basic Quantities: Derived Quantities: Length (m) Mass (kg) Time (s) Charge (C) : + or - Temperature (K) Luminous intensity (cd) Derived Quantities: Area, vol, density, vel, accel, etc. Force, (Newton: 1 N = 1 kg-m/s2) Work/Energy, (Joule: 1 J = 1 N-m) Power, (Watt: 1 W = 1 J/s) Current, (Ampere: 1 A = 1 C/s) Voltage, (Voltage: 1 V = 1 J/C) Decimal multiples and submultiples of SI units

A. FORCES Electrostatic Force – force due charges at rest Electrodynamic Force – due to charges in motion

B. CURRENT Current flow through a conductor Charge transport flow of electric charges: the amount of charge passing by a given point on a conductor per unit time Units:

Convention for direction: the direction of positive charge movement Positive ions Negative ions

The total charge entering a terminal is given to be Example1 The total charge entering a terminal is given to be mC. Calculate the current at s. Answer: 31.42 mA

Example 2. The current flowing through an element is Calculate the charge entering the element from 0 to 2 s. Answer: 6.667 C

C. VOLTAGE The voltage,ab, between points a and b is the work done (or change in energy) by the elecrical system in moving a unit charge from a to b. 1V = 1J/C The plus (+) and minus (-) signs are used to define reference direction or voltage polarity. The voltage can be interpreted in two ways: point a is at a potential of ab higher than b, or the potential at point a with respect to b is ab. Note:

Analogy in Mechanical Systems Potential Energy (per unit mass) due to Gravity

D. POWER and ENERGY Power is the time rate of expending or absorbing energy. For electrical systems Passive Sign Convention: positive: power is being delivered to or absorbed by the element negative: power is being supplied by the element.

Passive Sign Convention: When current arrow enters through the positive terminal of the element: use p = iv When current arrow enters through the negative terminal of the element: use p = -iv Both i and v can be + or – values. If p > 0 the element is absorbing power from circuit If p < 0 the element is delivering power to circuit i + – v i + – v p = +vi p = –vi

active or passive? Energy: absorbing or delivering? show pos current show higher V

The law of conservation of energy: The algebraic sum of power in a circuit at any time must be zero Energy is the capacity to do work, measured in joules (J). Energy absorbed or supplied by an element from to to t:

Example 3. An energy source forces a constant current of 2 A for 10 s to flow through a lightbulb. If 2.3 kJ is given off in the form of light and heat energy, calculate the voltage drop across the bulb. Answer: 115 V Example 4. How much energy does a 100-W bulb consume in two hours? Answer: 720 kJ, or 200 W-h

E. CIRCUIT ELEMENTS Active element – capable of generating electrical energy Passive element – can not generate energy Active Elements: Ideal Independent Source an active element that provides a specified voltage or current that is completely independent of other circuit elements.

1. Independent Voltage Source - delivers a voltage independent of the current - symbols are shown (a) for d.c., and (b) for either a.c. or d.c. v-i Characteristics (a) (b)

2. Independent Current Source - delivers a specified current that is independent of the voltage across the source - symbol is as shown for either a.c. or d.c. v-i Characteristics

Ideal Dependent (or Controlled) Source an active element in which the value of the source is controlled by another voltage or current. There are four types: A voltage-controlled voltage source (VCVS) A current-controlled voltage source (CCVS) A voltage-controlled current source (VCCS) A current-controlled current source (CCCS) Dependent sources are useful in modeling elements such as transistors, operational amplifiers and integrated circuits.

Dependent Sources (con’t) The figure below shows the four types of dependent sources: VCVS, CCVS, VCCS, and CCCS. The controlling variables c and ic are voltages and currents that appear elsewhere in the circuit.

Passive Elements: 1. RESISTOR Connect a copper wire to a generator. Vary voltage, and observe current. Ohm’s Law: =Ri R = resistance in ohms (Ω) 1 Ω = 1 V/A What happens? The application of voltage creates an electric field. Electrons try to accelerate, but collide with copper atoms and get scattered. But there is a net directed motion or “drift” of electrons to create the current. The higher the voltage, the higher the electric field, the higher the drift and current.

Resistance What determines R? depends on resistivity, length and cross-sectional area. ρ = resistivity in Ω-m (small for conductors, big for insulators) (1.72 X 10-8 for Cu, 6.4 X 102 for Silicon;1012 for glass) Mechanical Analogy: Fluid flow through a pipe

Conductance Conductance: i=G; G = 1/R = conductance in mhos or Siemens (S) Resistance of an element is a measure of its ability to resist the flow of electric current. Look at the v-i characteristic. v and i are proportional to each other.

Limiting Cases: Short Circuit and Open Circuit Short Circuit Open Circuit

2. Capacitor Take two flat copper plates separated by air as insulator. Apply a voltage; accumulates + and – charges. Measure the charge stored: q=C; C = capacitance in Farads (F); 1F = 1C/V

3. Inductor Take a coil wound around an iron core. Magnetic flux: L is the inductance in Henry (1 H = 1V-s/A) The voltage induced in a coil proportional to the rate of change of the magnetic flux.

Circuit Elements: Summary Active Elements Passive Elements A dependent source is an active element in which the source quantity is controlled by another voltage or current. They have four different types: VCVS, CCVS, VCCS, CCCS. Independent sources Dependent sources