Electric Circuit FE Exam Review

1
Electric Circuit FE Exam Review

• Y.T. Jade Morton

2
Topics To Be Covered

• Electric and Magnetic Quantities
• DC circuits
• AC circuits
• Electronic Circuits
• Transformers

3
Electric and Magnetic Quantities

• Static electric quantities
• Static magnetic quantities
• Resistance, voltage, current
• Power, energy, and measurements

4
Static Electric Quantities
Electric field generated by a point charge
E
r
Electric static force on a charge
Flux density
Q
Electric static force between two charges
r1
Q
Q
5
Example 1
Q210?C
Q1-4?C
1m
1m
A
B
1m
C

• Find
• The electric force on charge B
• The electric field at point C
• The electric field flux density at C due to
  charge A

6
Static Magnetic Quantities
A conductor of length L moving with velocity
v perpendicular to B has induced voltage VBLv
v
B
V
7
Example 2
Wire B
Wire A
1A
1A
1m
1m
X

• Find the magnetic flux density H at point X
• Find H if the wire A is bundled onto wire B
• Find H if wire A is removed, wire B is bent to
  form
• a circle centered at point X
• How will H change if wire b forms a double circle?

8
Voltage, Current, Power, Energy
Voltage
Current
Power
Electric power
9
Measurements
10
Example 3
Find the rms value for the periodic function i(t)
i(t)
3
2
1
6
7
8
9
2
3
5
1
4
t
11
Characteristics of R, C, L
12
Example 4
A sine wave of 10 volts rms value is applied to
a 10? resistor through a half wave rectifier.
What is the average value of the current?
13
DC Circuits

• KCL. KVL
• Analysis methods nodal, mesh
• Thevenin, Norton equivalent circuit
• Maximum power transfer
• First order RC and RL circuits

14
KCL and KVL
KCL At a circuit node, current in current
out or
KVL Around a closed loop, voltage rise voltage
drops or
15
Nodal Analysis

• Identify every node in the circuit.
• Select one node as the reference node.
• Ground node.
• The node with largest number of branches.
• Assign voltages v1, v2, , vn-1 to the remaining
  n-1 nodes.
• Apply KCL to each of the n-1 nodes. Using Ohms
  law to express branch currents in terms of node
  voltages.
• Solve the resulting equations to obtain the node
  voltages.
• Use ohms law to obtain branch currents.

16
Example 5
Find voltage V using nodal analysis
10O
6O
V1
20V
V
2O
V -
-
20V
4O
6A
17
Mesh Analysis

• Identify all meshes in a circuit
• Assign mesh currents i1, i2, in to the meshes.
• Apply KVL to each mesh. Use ohms law to express
  the voltages in terms of the mesh currents
• Solve the resulting equations to obtain the mesh
  currents.

18
Example 6
2O
9O
i
i1
-
i2
12V
-
12O
8V
4O
3O
Find current i in the circuit
19
Thevenins Equivalent Circuit
I
I
Linear network
RTh
V -
V -
RL
RL
VTh
VTh is the open circuit voltage of the linear
network RTh is the equivalent resistance of the
linear network
Maximum power transfer when RThRL , the
network delivers maximum power to RL
20
Nortons Equivalent Circuit
I
I
Linear network
V -
V -
RL
RL
IN
RN
IN is the closed circuit current of the linear
network RN is the equivalent resistance of the
linear network
Relationship between Thevenin and Norton theorems
RTh RN VTh In RN
21
Example 7
8O
a
4O
2A
5O
12V
8O
b
Find the Thevenin and Norton equivalent at
terminal ab. What is the load that will absorb
maximum power from this circuit.
22
First Order RC Circuit
Vc -
Where, ?RC
Steps 1. Find vc(0) 2. Find vc(?) 3. Find ?
23
First Order RL Circuit
Where, ?L/R
Steps 1. Find iL(0) 2. Find iL(?) 3. Find ?
24
Example 8
t0
6?
2?
v -
1/3F
10V
50V
The switch has been open for a long time and
then it is closed at t0. Find v for tgt0.
25
Example 9
1.5H
i
5?
10?
t0
3A
The switch has been closed for a long time. It
opens at t0. Find i(t) for tgt0
26
AC Circuits

• Sinusoids
• Phasors
• Impedance
• AC circuit analysis
• Resonators

27
Sinusoids and Phasors
Time domain
Sinusoid
Phasor domain
VVmej?
Phasor
Both representations contain critical sinusoids
information amplitude Vm and phase ?
28
Impedance
(?)
Impedance
I
i(t)
V -
v(t) -
Z
R, C or L
Phasor domain
Time domain
29
R, C, L ? Impedance
30
AC Circuit Analysis

• Transform every circuit element to their phasor
  representation
• Apply circuit laws, analysis methods, and
  theorems to the phasor domain circuit
• Solve for phasor domain circuit variables
• Transform these variables back to time domain.

31
Example 10
0.5H
10?
v0 -

0.05F
10cos(10t750)
Find v0
32
Example 11
R
L
vsVscos ?t
v0 -

C
Show that
33
Parallel Resonance
H(?)
1
B
?
?0
?1
?2
0
?
Resonance frequency
900
Bandwidth
00
?
?0
-900
Quality factor
34
Electronic Circuits

• 1. Diode
• 2. Rectifying circuits
• 3. Operational amplifiers

35
Diode
cathode
anode
i
-
V
V
0.40.7V
XX00 volts
36
Ideal Op Amp Equivalent Circuit
i10
2
6
v1 -
v0 -
i20
A(v2-v1)
-
v2 -
3
i10, i20 v2v1
37
Example 12
R1
-
v1
v0 -
v2
vi
38
Example 13
R1
v1
-
-
v1
v0 -
v0 -
v2
v2
vs1
is
vs2
39
Example 14
v1
R3
-
v0 -
v2
is
Prove