DC CIRCUITS
Ho Kyung Kim, Ph.D.
hokyung@pusan.ac.kr
School of Mechanical Engineering
Pusan National University
Basic Experiment and Design of Electronics
Outline
•Definition
•Serial vs. parallel circuits with resistances
•Kirchhoff’s law
•Voltage divider
•Loading effect
•Measuring devices
•Circuit analysis
2
Analogy btwn fluid & electricity
3
v
q
R
i
Ground
h
Q
Q
R
Ground
•Charge: fundamental electronic quantity
–elementary charges: electron, proton
–electronic charge, q = 1.602 1019
C
•Current:C/s or A
•Voltage or
potential difference
: 1 V = 1 J/C
•Ground: earth ground/chassis ground
•Power:J/s or W
•Source (energy
generation
) vs. load (energy
dissipation
)
–battery vs. a light bulb
Definition
dt
dq
i
CurrentVoltage
Time
Charge
Charge
Work
Time
Work
Power
R
V
RIVIP
2
2
•Circuit or network
•Source
–voltage
–current: DC vs. AC
•Branch
•Node
•Loop Mesh
•Network analysis
–to determine a
specific
voltage, current, or power
somewhere
in a network
•Resistance: constant of proportionality between the voltage and current
•Ohm's law
Resistor
A
l
v
i
v
1/R
i
RIV
A
l
A
l
I
V
R
= resistivity [cm]
=1/= conductivity [(cm)1
or S/cm]
–Electron drift velocity
–Current
–Conductance
l
V
Ev
eee
V
l
A
V
l
A
qn
l
V
AqnnvqAI
eee
)(
R
G
1
[S or mho]
GVI
–Algebraic sum of the currents leaving a node is zero
–Sum of currents entering node is equal to the sum of the currents leaving the node
–
Charge conservation law
•Algebraic sum of the currents entering any node is zero;
KCL: Kirchhoff's current law
0)(
1
N
j
j
ti
i1(t)
i5(t)
i4(t)
i3(t)
i2(t)
0)()()()()(
54321
tititititi
0)()()()()(
54321
tititititi
)()()()()(
43251
tititititi
•Algebraic sum of the voltages around any loop is zero;
–
energy conservation law
KVL: Kirchhoff's voltage law
0)(
1
N
j
j
tv
+
–
+
+

+
S
V
1R
V
2R
V
3R
V
0
321
RRRS
VVVV
•Series circuit
–Two or more circuit elements are said to be in
series
if the current from one element exclusively
flows into the next element
–From KCL, it then follows that all series elements have the
same current
•Parallel circuit
–Two or more circuit elements are said to be in
parallel
if the elements share the same terminals
–From KVL, it follows that the elements will have the
same voltage
Series vs. parallel circuits
Series circuit
–
+
+
–
+ –
–+
–
+
+
)(
1
tv
1R
v
2R
v
1
R
+

2
R
)(
5
tv
)(
2
tv
)(
3
tv
)(
4
tv
)(ti
0)()()()()()()(
1542321
tvtvtvtiRtvtvtiR
)()()()()()(
5432121
tvtvtvtvtvtiRR
+
–
)(tv
1
R
2
R
)(ti
≡v(t)
sum of several voltage sources in series can be replaced by one source
whose value is the algebraic sum of the individual sources
+
–
)(tv
S
R
)(ti
≡RS
equivalent resistance of
N
resistors in series
is simply the sum of the individual resistances
N
j
jS
RR
1
Parallel circuit
1
R
2
R
)(
1
ti
↑
↓
↑
↓
)(tv
+

)(
3
ti)(
4
ti)(
6
ti
)(
2
ti)(
5
ti
0)()()()()()(
654321
titititititi
)()()()()()(
526431
titititititi
↑
)(
0
ti
1
R
2
R
)(tv
+

sum of several current sources in parallel can be replaced by
one source whose value is the algebraic sum of the individual
sources
≡i0(t)
)(
11
21
tv
RR
↑
P
R
)(
0
ti
)(tv
+

N
j
jP
RR
1
11
P
R
tv)(
Voltage divider
12
+

)(tv
1R
v
2R
v
1
R
+
–
+

2
R
)(ti
KVL;
0)(
21
RR
vvtv
21
)(
RR
vvtv
Ohm's law;
)(
11
tiRv
R
)(
22
tiRv
R
Therefore,
)()()(
21
tiRtiRtv
21
)(
)(
RR
tv
ti
)()(
21
1
11
tv
RR
R
tiRv
R
)()(
21
2
22
tv
RR
R
tiRv
R
v(t)is divided between R1
and
R2
in direct proportion to their
resistances;
voltage divider
•Voltage divider: the voltage across each resistor in a series circuit is directly proportional
to the ratio of its resistance to the total resistance of the circuit
Divider rules
•Current divider: the current in a parallel circuit divides in inverse proportion to the
resistances of the individual parallel elements
S
Nn
n
n
i
RRRR
R
i
/1/1/1/1
/1
21
S
Nn
n
n
v
RRRR
R
v
21
Loading effect
+
–
V
in
= 30 V
R1
= 10 k
R2
= 10 k
V
out
= ?
V
in
R1
R2
V
out
R3
V
in
R1
R2
R3
V
in
R1
R2
 R3
V
out
•Ammeter
–current measuring device
–connected in
series
for the same current
–
zero
internal resistance required
•Voltmeter
–voltage measuring device
–connected in parallel for the same voltage
–
infinite
internal resistance required
•Ohmmeter
–resistance measuring device
–connected and functioned when the element is disconnected from any other circuit
Ohmmeter
Measuring devices
R
Ammeter
Voltmeter
Open and short circuits
V
+

I
V
+

I
I= 0for any V
R=
V= 0for any I
R= 0
•Or
network
analysis
•To determine a
specific
voltage, current, or power
somewhere
in a network
•Two methods
–Nodal analysis = node voltage method
–Loop analysis = mesh current method
Circuit analysis
Nodal analysis
•or node voltage method
①select a reference node (usually ground)
②define
n
–1 node voltages
③determine branch currents using Ohm's law
④apply KCLat each node
⑤solve the linear system
–
n
–1 –
m
unknowns if
m
voltage sources
①select a reference node
②define
n
–1 node voltages
11
1
R
v
R
vv
i
aca
2
2
R
vv
i
ba
33
3
R
v
R
vv
i
bcb
③determine branch currents
④apply KCL at each node
⑤solve the linear system
0
21
iii
S
0
32
ii
Sba
iv
R
v
RR
221
111
0
111
322
ba
v
RR
v
R
•or mesh current method
①define each mesh current
consistently
–e.g., clockwise direction
②apply KVLat each mesh
③solve the linear system
–
n
–
m
unknowns if
m
current sources
Loop analysis
①define each mesh current
②apply KVL at each mesh
③solve the linear system
0)(
22111
RiiRiv
S
0)(
4232212
RiRiRii
S
viRiRR
22121
)(
0)(
243212
iRRRiR
Selfassigned HW
•Rizzoni (5
th
ed.), Ch. 3
–1, 2, 3, 4, 7, 8, 9, 10, 11, 12
22
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