Exam 1 Review

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Exam 1 Review

• Chapters 1, 2, 9

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Charge, q
Recall Coulombs Law
Force F1 on charge q2 due to charge q1 is given by
Charge on an electron (proton) is negative
(positive) and equal to 1.602 x 10-19 C
Unit Newton meter2 / coulomb2 volt meter /
coulomb
Note Positive force is repulsive, negative
force is attractive
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Electric Current, i
Current (in amperes) (A) is the time rate of
change of charge q
1 A 1 C/s
Convention Direction of current flow is that of
positive charges, opposite to the
direction of electron flow
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Voltage
The energy in joules (w) required to move a
charge (q) of one coulomb through an element is 1
volt (V).
1 volt 1 joule/coulomb 1 newton meter/coulomb
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Power and Energy
Power (p), in watts (W), is the time rate of
expending or absorbing energy (w) in joules
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Power and Energy
Change in energy from time t1 to time t2
Passive sign convention
If p gt 0 power is absorbed by the element If p lt
0 power is supplied by the element

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Ohm's Law
Units of resistance, R, is Ohms (W)
R 0 short circuit
open circuit
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Conductance, G
Unit of G is siemens (S),
1 S 1 A/V
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Power
A resistor always dissipates energy it
transforms electrical energy, and dissipates it
in the form of heat. Rate of energy dissipation
is the instantaneous power
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Elements in Series
Two or more elements are connected in series if
they carry the same current and are connected
sequentially.
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Elements in Parallel
Two or more elements are connected in parallel if
they are connected to the same two nodes
consequently have the same voltage across them.
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Kirchoffs Current Law (KCL)
The algebraic sum of the currents entering a node
(or a closed boundary) is zero.
where N the number of branches connected to the
node and in the nth current entering (leaving)
the node.
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Sign convention Currents entering the node are
positive, currents leaving the node are negative.
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Kirchoffs Current Law (KCL)
The algebraic sum of the currents entering (or
leaving) a node is zero.
Entering
Leaving
The sum of the currents entering a node is equal
to the sum of the currents leaving a node.
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Kirchoffs Voltage Law (KVL)
The algebraic sum of the voltages around any loop
is zero.
where M the number of voltages in the loop and
vm the mth voltage in the loop.
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Sign convention The sign of each voltage is the
polarity of the terminal first encountered in
traveling around the loop.
The direction of travel is arbitrary.
Clockwise
Counter-clockwise
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Series Resistors


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Voltage Divider
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Parallel Resistors
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Current Division
Current divides in inverse proportion to the
resistances
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Current Division
N resistors in parallel
Current in jth branch is
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Source Exchange
We can always replace a voltage source in series
with a resistor by a current source in parallel
with the same resistor and vice-versa. Doing
this, however, makes it impossible to directly
find the original source current.
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3-bit R2-R Ladder Network
KCL
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Writing the Nodal Equations by Inspection

• The matrix G is symmetric, gkj gjk and all of
  the off-diagonal terms are negative or zero.

The gkk terms are the sum of all conductances
connected to node k.
The gkj terms are the negative sum of the
conductances connected to BOTH node k and node j.
The ik (the kth component of the vector i) the
algebraic sum of the independent currents
connected to node k, with currents entering the
node taken as positive.
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Writing the Mesh Equations by Inspection

• The matrix R is symmetric, rkj rjk and all of
  the off-diagonal terms are negative or zero.

The rkk terms are the sum of all resistances in
mesh k.
The rkj terms are the negative sum of the
resistances common to BOTH mesh k and mesh j.
The vk (the kth component of the vector v) the
algebraic sum of the independent voltages in mesh
k, with voltage rises taken as positive.
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Turning sources off
Current source
We replace it by a current source where
An open-circuit
Voltage source
We replace it by a voltage source where
i
An short-circuit
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Thevenin's Theorem
Thevenins theorem states that the two circuits
given below are equivalent as seen from the load
RL that is the same in both cases.
VTh Thevenins voltage Vab with RL
disconnected ( ?) the open-circuit voltage
VOC
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Thevenin's Theorem
RTh Thevenins resistance the input
resistance with all independent sources turned
off (voltage sources replaced by short circuits
and current sources replaced by open circuits).
This is the resistance seen at the terminals ab
when all independent sources are turned off.
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Thevenin Example (Using Voc Isc)
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Maximum Power Transfer
What is the resistance of the load that will
result in the maximum power being delivered to
the load?
Consider the source to be modeled by its Thevenin
equivalent.
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Thus, maximum power transfer takes place when the
resistance of the load equals the Thevenin
resistance RTh. Note also that
Thus, at best, one-half of the power is
dissipated in the internal resistance and
one-half in the load.
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Ideal Op Amp
1)
The open-loop gain, Av, is very large,
approaching infinity.
2)
The current into the inputs are zero.
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Ideal Op Amp with Negative Feedback
Golden Rules of Op Amps

1. The output attempts to do whatever is necessary
   to make the voltage difference between the inputs
   zero.
2. The inputs draw no current.

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Non-inverting Amplifier
Closed-loop voltage gain
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Inverting Amplifier
Current into op amp is zero