Basic Electrical Theory

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Chapter 1

• Basic Electrical Theory

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1.1 Introduction to Electrical Engineering

• Electrical Engineering harnesses electrical
  energy for human good for transporting energy
  and information, for lifting the burdens of toil
  and tedium (motors).
• Foundational Ideas in Electrical Engineering
• 1. Conservation of charge (Kirchhoffs current
  law) is one of the principles used in writing
  circuit equations.
• 2. Conservation of energy (Kirchhoffs voltage
  law) is one of the fundamental principles used in
  writing circuit equations, and conservation of
  energy.
• 3. The frequency domain is a way of looking at
  the physical world in which frequency, not time,
  is the independent variable.

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Foundational Ideas in Electrical Engineering

• 4. Equivalent circuits model real devices by
  ideal electrical devices that have identical or
  similar characteristics.
• 5. Impedance level determines how electrical
  devices interact.
• 6. Feedback is a technique for bringing part of
  the output of an electronic device back to the
  input to improve performance.
• 7. Analog information uses an electrical signal
  proportional to the information content.
• 8. Digital information uses a two-valued code to
  represent the information content.

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Circuit Theory

• Practically every electrical device is a circuit.
• A radio is a circuit, as is the power
  distribution system that runs your lights and air
  conditioner.
• Hence, understanding of the methods of circuits
  opens the door to all the areas of electrical
  engineering.

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1.2 Physical Basis of Circuit Theory

• Charge, like mass, is a property of matter.
• The unit of electric charge is the coulomb (C),
  named in honor of Charles de Coulomb.
• There are two types of charge, positive and
  negative.
• Traditionally the electron has been assigned a
  negative sign, and the proton a positive.
• The magnitude of the charge on an electron is
• e - 1.602 X 10-19 coulombs (C)

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1.2 Physical Basis of Circuit Theory

• Forces between charges and Energy
• Charges attract or repel each other due to
  electrostatic forces. Electrostatic forces are
  responsible for lightening.
• Magnetic forces depend on moving charges
  (current). Magnetic forces turn motors, and
  effect energy conversion in generators.
• Energy is the medium of exchange in a physical
  system, like money is in an economic system.
• In mechanics, it takes force and movement to do
  work (exchange energy).
• In electricity, it takes electrical force
  (voltage) and movement of charges (current) to do
  work (exchange energy).

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1.2 Physical Basis of Circuit Theory

• Circuit Theory
• Consider a circuit consisting of a battery,
  light, switch, two headlights, and connecting
  wires and chassis from a car, as shown in fig
  1.1(page 6).
• When we pull the switch, the lights will glow and
  get hot, which suggests the battery is supplying
  energy to the headlights.
• Figure 1.2 (page 7) shows an electric circuit
  representing the physical situation shown in fig.
  1.1.
• We can use circuit theory to calculate the
  current in the wires, the power out of the
  battery, and the power into each headlight.
• The solution of an engineering problem normally
  proceeds through four stages First, a real world
  problem is identified second, the problem is
  modeled third, the model is analyzed and forth,
  the results are applied to the original physical
  problem.

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1.3 Current and Kirchhoffs Current Law

• Current is charge in motion.
• Current I ?Q/ ?t C/s or ampere, A
• To specify a current we require a reference
  direction plus a numerical value (fig 1.4, page
  8).
• Velocity is the simplest mechanical analogy for
  electric current, and displacement would be
  analogous to charge accumulation.
• q t1?t2i(t) dt coulombs fig 1.5, page 9.

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1.3 Current and Kirchhoffs Current Law

• Kirchhoffs Current Law
• The sum of currents entering a node is equal to
  the sum of currents leaving the node.
• i1 i2 i3 i4 - Fig 1.6, page 11.
• Example 1.2, page 11
• i1 i2 iL
• 8 i2 12
• I2 12 8 4 A

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1.4 Voltage and Kirchhoffs Voltage Law

• Voltage is defined as the potential for doing
  work. It measures how much work would be done by
  the electrical system in moving a charge from one
  point to another in a circuit, divided by the
  charge.
• V ab work done by the electrical system in
  moving q from a to b / q
• The unit is energy/charge, joules per coulomb or
  volt (V) to honor Count Volta.
• Force is a mechanical analog for voltage.

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1.4 Voltage and Kirchhoffs Voltage Law

• Kirchhoffs voltage law The voltage sum around a
  closed loop is zero.
• ?loop voltages 0
• In writing KVL equations, we write the voltage
  with a positive sign if the is encountered
  before the and with a negative sign if the is
  encountered first as we move around the loop.
• In fig 1.9, page 16 -12.6 vsw vL 0

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1.5 Energy Flow in Electrical Circuits

• Power is defined as the rate of energy exchange.
  Power is by definition the product of voltage and
  current.
• v (work/charge) x i (charge /time)
  work/ time power (1.30)
• The unit for power is watts (W).

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1.5 Energy Flow in Electrical Circuits

• Energy W t1?t2 p dt t1?t2 vab i dt Joules
• Example 1.7, page 22
• p vi 12.6 x 60 756 W
• Energy W 0?10 p dt 10 p 7560 J

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1.6 Circuit Elements Resistance and Sources

• Ohms Law v iR or i v/R . (1.41)
• R is the resistance and has a unit of volt per
  ampere, but we use the unit ohm to honor Ohm,
  abbreviated by the Greek letter omega, O .
• The resistance of a piece of wire is directly
  proportional to its length to the property of the
  material called resistivity, and inversely
  proportional to its cross sectional area.
• R ? l / A
• Where ? (rho) the resistivity, l is the length,
  and A the area of the wire.
• Table 1.1, page 24 Property of copper wires,
  gage size (smaller the gage size, higher the
  current limit).

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1.6 Circuit Elements Resistance and Sources

• Conductance
• Is the reciprocal of resistance.
• Conductance G 1 / R
• The unit is Siemens (S) and symbol is mho (upside
  down O).
• Power in resistance
• p vi (R i) i i2R v ( v/R) v2 /R
  (1.44)
• Do example 1.8, page 25.

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1.6 Circuit Elements Resistance and Sources

• Open circuits and short circuits
• Fig 1.19, page 25.
• A short circuit (R0) permits current to flow
  without any resulting voltage (v0).
• An open circuit (R8) permits voltage with no
  current (i0).
• In both cases eq. (1.44) shows that no power is
  required for the open or short circuit.

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1.6 Circuit Elements Resistance and Sources

• Switches
• An ideal switch is a special resistance that can
  be changed from a short circuit to an open
  circuit to turn an electrical device ON or OFF.
• Fig 1.20(a), page 26 shows a single pole, single
  throw switch in its open (OFF) state.
• Fig 1.20(b) shows a single pole, double throw
  switch, which switches one input line between two
  output lines.
• Fig 1.20(c) shows a double pole, single throw
  switch the dashed line indicates mechanical
  coupling between the two components of the switch
  to cause simultaneous switching.
• Switches can have any number of poles and throws.

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1.6 Circuit Elements Resistance and Sources

• Ideal voltage source
• Fig 1.21, page 27 shows the circuit symbol,
  mathematical definition, and graphical
  characteristic of an ideal general and dc voltage
  source.
• The ideal voltage source maintains its prescribed
  voltage, independent of its output current.

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1.6 Circuit Elements Resistance and Sources

• Ideal current source
• Fig 1.22, page 27 shows the circuit symbol,
  mathematical definition, and graphical
  characteristic of an ideal general and dc current
  source.
• The ideal current source maintains its prescribed
  current, independent of its output voltage.

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1.6 Circuit Elements Resistance and Sources

• Analysis of DC Circuits
• Headlight circuit fig 1.24, page 29.
• Going clockwise around the left loop
• -12.6 vsw vL 0
• KVL clockwise around the loop created by the
  resistors is
• - vL vR 0
• We must solve these equations for two cases the
  switch open (OFF) and the switch closed (ON).
• With the switch OFF no current flows, vL vR
  0 and
• -12.6 vsw 0 0. So vsw 12.6 V
• With the switch ON vsw 0, and we get vL vR
  12.6V
• The current iL vL/ RL 12.6 V/ 5.25 O 2.40 A
  iR
• Current in the battery Applying KCL iL iR
  iB 2.4 2.4 4.8A
• The power out of the battery pout 12.6V X 4.8
  A 60.5 W
• Power in each resistance pL pR 12.6 V X 2.4
  A 30. 25 W

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1.7 Series and Parallel Resistances Voltage and
Current Dividers

• Series Resistances and Voltage Dividers
• Two circuit elements are connected in series when
  the same current flows through them.
• Fig 1.28, page 33 shows a series connection of
  three resistances and a battery.
• We can write KVL around the loop going clockwise
• -Vs v1 v2 v3 0
• Or Vs V1 v2 V3
• Or Vs iR1 iR2 iR3 (using Ohms Law)
• Vs (R1 R2 R3) I
• Vs Req I
• Resistances in series Req R1 R2 R3

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1.7 Series and Parallel Resistances Voltage and
Current Dividers

• Voltage Dividers
• Current i Vs/ Req
• Vi R1 X i R1 / Req X Vs .(1.66)
• Where Req R1 R2 R3(for series circuits)
• The circuit of fig 1.30, page 34 models a
  flashlight. Calculate the voltage across the 2.5
  O resistance representing the flashlight bulb
  (Vb) when the switch is closed.
• Applying KVL - 1.5 0.3 i 1.5 .3 i Vsw
  2.5 i 0
• With the switch closed
• Vsw 0 and i 3.0/(0.3 0.3 2.5)
• Vb 2.5 i 2.42 V

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1.7 Series and Parallel Resistances Voltage and
Current Dividers

• Parallel Resistances
• Resistances are said to be connected in parallel
  when they have the same voltage across them.
• Fig 1.31, page 36 shows a parallel combination of
  three resistances and a current source.
• KCL for node A Is i1 i2 i3
• Is v/R1 v/R2 v/R3
• Is v ( 1/ R1 1/ R2 1/ R3)
• Is v ( 1/ Req) where
• 1/ Req 1/ R1 1/ R2 1/ R3
• Req (1/ (1/ R1 1/ R2 1/ R3) ..(1.74)

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1.7 Series and Parallel Resistances Voltage and
Current Dividers

• Current Dividers (page 37)
• V Req Is
• i1 v/R1 Req Is/ R1
• (1/R1 / 1/ R1 1/ R2 1/ R3) Is
• In general
• Ii 1/Ri / 1/ R1 1/ R2 1/ R3..) It
  (1.76)
• Where It is the total current entering the
  parallel combination.
• Example 1.11 page 37
• Req (4 4) II (8 4) 4.8 O
• Voltage across combination is 5 X 4.8 24 V

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Home Work

• 1. What is electrical engineering?
• 2. What are the foundational ideas in electrical
  engineering?
• 3. What is a circuit? Give examples.
• 4. Explain energy. Give examples.
• 5. What are the four stages to the solution of an
  engineering problem?
• 6. What is current? Give its formula with units.
  What is its mechanical analog?
• 7. Define Kirchhoffs current law.
• 8. What is voltage? Give its formula with units.
  What is its mechanical analog?
• 9. Define Kirchhoffs voltage law.
• 10. What is power? Give its formula with units.
• 11. What is energy? Give its formula with units.
• 12. What is Ohms law.
• 13. Explain conductance.
• 14. What are the several ways to express power in
  resistance.
• 15. Define open and short circuit.
• 16. What is the formula for resistances in
  series?
• 17. What is the formula for resistances in
  parallel?

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Test Study Questions

• 1. Page 19, problem 3.
• 2. Page 23, problem 3.
• 3. Page 33, problem 2.
• 4. Page 40, problem 4.