LECTURE : REVIEW OF BASIC CIRCUITS CONCEPTS

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LECTURE REVIEW OF BASIC CIRCUITS CONCEPTS

• September 28, 2009

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REVIEW OF BASIC CIRCUITS CONCEPTS ELECTRICAL
QUANTITIS

Charge, Current, and Voltage

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REVIEW OF BASIC CIRCUITS CONCEPTSELECTRICAL
QUANTITIS

• Charge is measured in coulombs .
• Current is a flow of electrical charge from one
  region to another.
• Currents not only have magnitude, but also have
  direction.
• To indicate its direction, a current is described
  by a number with a sign.

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REVIEW OF BASIC CIRCUITS CONCEPTSELECTRICAL
QUANTITIS
Current in a wire has its value and the
reference direction (direction of the arrow).
Choice of the reference direction is
arbitrary. By definition, a current is positive
when positive charges move in the reference
direction. If I is a negative number, this
means that current flows in the direction
opposite to the direction of the arrow.
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REVIEW OF BASIC CIRCUITS CONCEPTSELECTRICAL
QUANTITIS

• Electrical Potential and Voltage
• When electrical forces act on a charged particle,
  it will possess potential energy the value of it
  depends on the particle location.
• The potential energy can be turn into kinetic
  energy by releasing the particle.
• After a while the particle will reach a position
  where its potential energy is lower, and the
  potential energy difference will be converted to
  kinetic energy.

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REVIEW OF BASIC CIRCUITS CONCEPTSELECTRICAL
QUANTITIS

• To describe the potential energy that a particle
  with a charge will have at point , the
  electric potential is defined as
• where is the potential energy of the
  particle with charge at the position .
• IMPORTANT The zero point of potential energy can
  be arbitrarily chosen. The reason for this is
  that only differences in potential energy have
  practical meaning.

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REVIEW OF BASIC CIRCUITS CONCEPTSELECTRICAL
QUANTITIS

• We can choose any point in a circuit to be the
  point where electrical potential is zero. This
  point is referred as the ground point.
• Just as with potential energy, it is the
  differences of electrical potential that matter.
  
• The term voltage is used for difference in
  electric potential.
• Voltages can either positive or negative numbers
  and are measured in volts ( ). It is usual to
  express all potentials with respect to the
  ground.
• The potential difference between any point and
  ground is called the voltage at that point. The
  words voltage at point A always mean the
  potential at point A with respect to ground. The
  symbol for this voltage is .

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REVIEW OF BASIC CIRCUITS CONCEPTSELECTRICAL
QUANTITIS

If there is a circuit element with voltage
indication with and signs, that means that
the indicated voltage is equal to the potential
at the sign minus the potential at the sign.
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REVIEW OF BASIC CIRCUITS CONCEPTSProblem

(the potential at A with respect to the ground)
is 4V. And
?
What is
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PROBLEM
In Fig. (a), the current I1 is -2mA. Is it
possible to say what I2 is and why?
In Fig. (b), the current I1 is 2mA. Is it
possible to say what I2 is and why?
Is it possible to say what I3 is and why?
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REVIEW OF BASIC CIRCUITS CONCEPTS

• Circuit elements Wires, voltage sources, current
  sources, resistors, capacitors, inductors,
• We will assume that wires are ideal (perfect
  conductors) and all points along a wire are at
  exactly the same potential.
• Open circuit exists between two points when they
  are not connected together by any circuit
  element. No current can flow through the open
  circuit.
• Short circuit exists between two points when they
  are connected together by an ideal wire. Both
  points have the same voltage.
• Additional terms Nodes and loops.

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REVIEW OF BASIC CIRCUITS CONCEPTSKIRCHHOFFS LAWS

• KCL The algebraic sum of the currents entering
  and leaving
• a junction is zero
• KVL The algebraic sum of the changes in
  potential around a
• closed loop is zero

I2
I1
I1I2I3
I3
http//www.rfcafe.com/references/electrical/kirchh
offs_law.htm
b
c
0(Vb-Va)(Vc-Vb)(Vd-Vc)(Va-Vd)
a
d
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REVIEW OF BASIC CIRCUITS CONCEPTSDC CIRCUIT
ANALYSIS

• The circuit elements Ideal resistors, Ideal
  voltage and current sources.
• Ideal voltage source
• Ideal current source
• Ideal resistor is described by Ohms law
• The algebraic signs of voltage and current are
  very important.
• Useful First choose the reference direction for
  current through the resistor. The value of this
  current is the potential at the tail of the arrow
  minus the potential at the head of the arrow,
  divided by R.
• Try memorizing this rule.

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REVIEW OF BASIC CIRCUITS CONCEPTSDC CIRCUIT
ANALYSIS

• How we should choose a sign of each voltage in
  the circuit?
• KVL

As a result, KVL has the form
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REVIEW OF BASIC CIRCUITS CONCEPTSRESISTORS IN
SERIES

• Two resistors in series

II1I2
V0V1V2
Ohms law for each element VIR
V0I1R1I2R2 Ohms law for complete
circuit V0IReq
ReqR1R2
gt
It is the voltage that is divided between
elements in series.
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REVIEW OF BASIC CIRCUITS CONCEPTSRESISTORS IN
PARALLEL

• Two resistors in parallel
• Resistors are connected in such a way that
  they branch out from a single
• node

VV1V2
II1I2
V/ReqV1/R1V2/R2
gt
1/Req1/R11/R2
It is the current that is divided between the
elements in parallel.
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POWER IN RESISTORS

• The power dissipated by a resistor
• PIV or I2R
• Circuit is
• short if R0
• open if Rinfinity

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REVIEW OF BASIC CIRCUITS CONCEPTSAC CIRCUIT
ANALYSIS

• Everything we have learned about DC analysis
  remains true in the AC, or time-varying, case.
• The circuit elements - ideal voltage sources,
  current sources, and resistances - behave in the
  same way whether or not the voltages vary in
  time.
• Additional elements that are useful only in AC
  circuits capacitors and inductors.
• Sometimes interaction of AC signals with
  inductors and capacitors can provide striking
  results How the very large voltages - tens kV -
  can appear in the sparkplug in a car where power
  is supplied by a battery of 12 V?
• This amazing voltage transformation is usually
  obtained by using a single inductor.

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REVIEW OF BASIC CIRCUITS CONCEPTS IDEAL CAPACITOR

• Basic physics of the capacitor lies in the fact
  that the voltage across the capacitor is linearly
  proportional to the charge on its plates.
• QCV gt IdQ/dtCdV/dt
• We have to specify algebraic signs. We will adopt
  the same nomenclature used for resistances.

In dc circuits capacitors behave just like an
open circuit.
Just as with Ohms law, the algebraic signs of
the current and voltage are of greatest
importance.
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CAPACITORS

• Two capacitors in parallel
• I C1dV/dt C2dV/dt (C1 C2)dV/dt
• Cpar C1 C2
• Two capacitors in series
• I C1dV1 /dt C2dV2 /dt
• dV/dt dV1 /dt dV2 /dt dV1 /dt C1/C2 dV1
  /dt (1 C1/C2)dV1 /dt
• dV1 /dt I/ C1 Cser C1 C2 /(C1 C2)

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REVIEW OF BASIC CIRCUITS CONCEPTS IDEAL INDUCTOR

• The I-V relationship

If current through an inductor is constant, the
voltage across the inductor will be zero.
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RC CIRCUITS, CHARGING CAPACITOR
For tlt0 switch was in position b and at t0 it
moved in position a.
KVL Vb-VR-VC0 VRIR ICdVC/dt
vR
Solution of non-homogeneous diff. eq-n is sum of
general solution of homogeneous equation and
particular solution of non-homogeneous equation.
Since Vbconst, particular solution is VConstVb
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RC CIRCUITS, CHARGING CAPACITOR
At t0 V0 gt A -Vb
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RC CIRCUITS, DISCHARGING CAPACITOR
For tlt0 switch was in position a and at t0 it
moved in position b.
KVL
VR
VR IR
At t0 VVbgt AVb
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SUMMARY CHARGING AND DISCHARCHING A CAPACITOR