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Analogue electronics
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Lecture 2
Basic Circuit Laws
2
Basic Circuit Laws
2.1 Ohm’s Law.
2.2 Nodes, Branches, and Loops.
2.3 Kirchhoff’s Laws.
2.4 Series Resistors and Voltage Division.
2.5 Parallel Resistors and Current Division.
2.6 Wye-Delta Transformations.
3
2.1 Ohms Law (1)
• Ohm’s law states that the voltage across a resistor V(v) is directly proportional to the current I(A) flowing through the resistor.
• When R=0 short circuit
• When R= open circuit.
IR
IRV
R
R
IV
VVV
ab
ab
baab
Resistance
alityproportion ofconstant
a
b
4
2.1 Ohms Law (2)• Conductance is the ability of an element to
conduct electric current; it is the reciprocal of resistance R and is measured in siemens.
• The power dissipated by a resistor:
v
i
RG
1
R
vRivip
22
5
2.4 Series Resistors and Voltage Division (1)
• Series: Two or more elements are in series if they are cascaded or connected sequentially and consequently carry the same current.
• The equivalent resistance of any number of resistors connected in a series is the sum of the individual resistances.
• The voltage divider can be expressed as
N
n
nNeq RRRRR1
21
vRRR
Rv
N
n
n
21
321)(
321)(
VVVV
IIII
Totalseries
Totalseries
As the current goes through the circuit, the charges must USE ENERGY to get
through the resistor. So each individual resistor will get its own individual potential
voltage). We call this voltage drop.
is
series
seriesTT
Totalseries
RR
RRRR
RIRIRIRI
IRVVVVV
321
332211
321)(
)(
;Note: They may use the
terms “effective” or
“equivalent” to mean
TOTAL!
2.4 Series Resistors and Voltage Division
(1)
ExampleA series circuit is shown to the left.
a) What is the total resistance?
b) What is the total current?
c) What is the current across EACH resistor?
d) What is the voltage drop across each resistor?( Apply Ohm's law to each resistor separately)
R(series) = 1 + 2 + 3 = 6W
V=IR 12=I(6) I = 2A
They EACH get 2 amps!
V1W(2)(1) 2 V V3W=(2)(3)= 6V V2W=(2)(2)= 4V
Notice that the individual VOLTAGE DROPS add up to the TOTAL!!
8
2.5 Parallel Resistors and Current Division (1)
• Parallel: Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them.
• The equivalent resistance of a circuit with N resistors in parallel is:
• The total current i is shared by the resistors in inverse proportion to their resistances. The current divider can be expressed as:
Neq RRRR
1111
21
n
eq
n
nR
iR
R
vi
2.5 Parallel Resistors and Current Division (1)
• Parallel wiring means that the devices are connected in such a way
that the same voltage is applied across each device.
• Multiple paths are present.
• When two resistors are connected in parallel, each receives current
from the battery as if the other was not present.
• Therefore the two resistors connected in parallel draw more current
than does either resistor alone.
321
321
321
321
1111
)(
;
RRRR
R
V
R
V
R
V
R
V
R
VIIIII
IRVVVVV
p
parallel
parallelT
Total
R3
i iP RR
11
I3
Example 4
454.0
1454.0
1
9
1
7
1
5
11
P
p
P
RR
R
)(8 RI
IRV
To the left is an example of a parallel circuit.
a) What is the total resistance?
b) What is the total current?
c) What is the voltage across EACH resistor?
d) What is the current drop across each resistor?
(Apply Ohm's law to each resistor separately)
2.20 W
3.64 A
8 V each!
WWW9
8
7
8
5
8975 III
IRV
1.6 A 1.14 A 0.90 A
Notice that the
individual currents
ADD to the total.
11
Gustav Kirchhoff
1824-1887
German Physicist
12
2.2 Nodes, Branches and Loops (1)
A branch represents a single element such as a
voltage source or a resistor.
A node is the point of connection between two
or more branches.
A loop is any closed path in a circuit.
13
2.2 Nodes, Branches and Loops (2)
Example 1
How many branches, nodes and loops are there?
4 Branches
3 Nodes
4 loops
Original circuitEquivalent circuit
14
2.2 Nodes, Branches and Loops (3)
Example 2 Should we consider it as one
branch or two branches?
How many branches, nodes and loops are there?
7 Branches
4 Nodes
4 loops
15
2.3 Kirchhoff’s Laws (1)
Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a node (or a closed boundary) is zero.
01
N
n
niMathematically,
Junction Rule
Conservation of mass
Electrons entering must
equal the electrons leaving
The junction rule states
that the total current
directed into a junction
must equal the total current
directed out of the junction.
Kirchhoff’s Current Law
At any instant the algebraic sum of the
currents flowing into any junction in a circuit is
zero
For exampleI1 – I2 – I3 = 0
I2 = I1 – I3
= 10 – 3
= 7 A
18
2.3 Kirchhoff’s Laws (3)
Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is
zero.
Mathematically, 01
M
m
nv
Kirchhoff’s Voltage Law
At any instant the algebraic sum of the
voltages around any loop in a circuit is zero
For example
E – V1 – V2 = 0
V1 = E – V2
= 12 – 7
= 5 V
Example 14 Using Kirchhoff’s Loop Rule
Determine the current in the circuit.
( ) ( ) 21
drops potentialrises potential
0.8V 0.6 12V 24 WW II
A 90.0
I 20 V 18
I
i
iV 0
( )321 VVVVbattery
21
2.3 Kirchhoff’s Laws (4)Example 5
Applying the KVL equation for the circuit of the figure below.
Va-V1-Vb-V2-V3 = 0
V1 = IR1 V2 = IR2 V3 = IR3
Va-Vb = I(R1 + R2 + R3)
321 RRR
VVI ba
Loop Rule
The loop rule expresses conservation of
energy in terms of the electric potential.
States that for a closed circuit loop, the total
of all potential rises is the same as the total of
all potential drops.