# 1 1 5 CircuitTheoryLaws Notes ```Bhuvi Alluri
Circuit Theory Laws
Digital Electronics
&copy; 2018 Project Lead The Way, Inc.
Circuit Theory Laws
This presentation:
• Reviews voltage, current, and resistance.
• Reviews and applies Ohm’s Law.
• Reviews series circuits.
o Current in a series circuit
o Resistance in a series circuit
o Voltage in a series circuit
• Reviews and applies Kirchhoff’s Voltage Law.
• Reviews parallel circuits.
o Current in a parallel circuit
o Resistance in a parallel circuit
o Voltage in a parallel circuit
• Reviews and applies Kirchhoff’s Current Law.
2
Electricity – The Basics
An understanding of the basics of electricity
requires the understanding of three fundamental
concepts.
• Voltage
• Current
• Resistance
A direct mathematical relationship exists
between voltage, resistance, and current in all
electronic circuits.
3
Voltage
Voltage is the electrical force that causes
current to flow in a circuit.
Voltage is measured in volts.
Alessandro Volta
1745–1827
Italian Physicist
4
Voltage, Current, and Resistance
Current is the flow of electrical charge through
an electronic circuit. The direction of a current
is opposite to the direction of electron flow.
Current is measured in amperes (amps).
Andre Ampere
1775–1836
French Physicist
5
Resistance
Resistance is a measure of opposition to
current flow.
Resistance is measured in ohms.
Georg Simon Ohm
1789–1854
German Physicist
6
First, An Analogy
The flow of water from one tank to another is a good
analogy for an electrical circuit and the mathematical
relationship between voltage, resistance, and current.
Force
The difference in the water levels ≡ Voltage
Flow
The flow of the water between the tanks ≡ Current
Opposition The valve that limits the amount of water ≡ Resistance
Force
Flow
Opposition
7
Anatomy of a Flashlight
Switch
Switch
Light
Bulb
Battery
Block Diagram
Light
Bulb
-
+
Battery
Schematic Diagram
8
Flashlight Schematic
Current
Resistance
-
+
-
Voltage
+
•
Closed circuit (switch closed)
•
Open circuit (switch open)
•
Current flow
•
No current flow
•
Lamp is on
•
Lamp is off
•
Lamp is resistance, using
energy to produce light (and
heat)
•
Lamp is resistance, but is not
using any energy
9
Current Flow
• Conventional Current assumes
that current flows out of the
positive side of the battery,
through the circuit, and back to
the negative side of the battery.
This convention was established
when electricity was first
discovered, but it’s incorrect!
• Electron Flow is what actually
happens. The electrons flow out
of the negative side of the battery,
through the circuit, and back to
the positive side of the battery.
Conventional
Current
Electron
Flow
10
Engineering vs. Science
• Both Conventional Current and Electron Flow are ways to
describe electricity. In general, the science disciplines use
Electron Flow, whereas the engineering disciplines use
Conventional Current.
• Since this is an engineering course, we use Conventional
Current.
• The direction that the current flows does not affect the result;
thus, it doesn’t make any difference which convention you use
as long as you’re consistent.
Electron
Flow
Conventional
Current
11
Ohm’s Law
• Defines the relationship between voltage, current, and
resistance in an electric circuit
• Ohm’s Law:
Current in a resistor varies in direct proportion to the voltage
applied to it and is inversely proportional to the resistor’s value.
• Stated mathematically:
V
I=
R
+
I
V
-
R
Where: I is the current (amperes)
V is the potential difference (volts)
R is the resistance (ohms)
Ohm’s Law Triangle
V
I
R
V
I
R
V
I
V
I=
(amperes, A )
R
R=
V
(ohms, W)
I
V = I R ( volts, V )
R
Example: Ohm’s Law
Example:
The flashlight uses a 6 volt battery and has a bulb with a
resistance of 150 W. When the flashlight is on, how much
current will be drawn from the battery?
14
Example: Ohm’s Law
Example:
The flashlight uses a 6 volt battery and has a bulb with a
resistance of 150 W. When the flashlight is on, how much
current will be drawn from the battery?
Solution:
Schematic Diagram
VT =
IR
V
+
-
VR
VR
6V
IR =
=
= 0.04 A = 40 mA
R 150 W
I
R
15
Circuit Configuration
Components in a circuit can be connected in one of two
ways.
Series Circuits
Parallel Circuits
• Components are connected
end-to-end.
• There is only a single path for
current to flow.
• Both ends of the components
are connected together.
• There are multiple paths for
current to flow.
Components
(resistors, batteries, capacitors, etc.)
16
Circuit Configuration
Combination Circuit: A circuit that contains
components that are connected in both series
and parallel
17
Series Circuits
Characteristics of a series circuit
• The current flowing through every series component is equal.
• The total resistance (RT) is equal to the sum of all of the resistances
(R1 + R2 + R3).
• The sum of all of the voltage drops (VR1 + VR2 + VR2) is equal to the
total applied voltage (VT). This is called Kirchhoff’s Voltage Law.
VR1
IT
+
-
+
+
VR2
VT
-
-
RT
-
+
VR3
18
Example: Series Circuit
Example:
For the series circuit shown, use the laws of circuit theory to calculate
the following:
• The total resistance (RT)
• The current flowing through each component (IT, IR1, IR2, and IR3)
• The voltage across each component (VT, VR1, VR2, and VR3)
• Use the results to verify Kirchhoff’s Voltage Law.
IT
+
VR1
-
IR1
+
+
VT
VR2
IR2
-
-
IR3
RT
-
+
VR3
19
Example: Series Circuit
Solution:
Total Resistance:
R T = R1 + R2 + R3
R T = 220 W + 470 W + 1.2 kW
R T = 1890 W = 1.89 kW
Current Through Each Component:
IT =
VT
RT
(Ohm' s Law)
12 v
IT =
= 6.349 mAmp
1.89 kW
V
I
R
Since this is a series circuit :
IT = IR1 = IR2 = IR3 = 6.349 mAmp
20
Example: Series Circuit
Solution:
Voltage Across Each Component:
VR1 = IR1 &acute; R1 =
(Ohm' s Law)
VR1 = 6.349 mA &acute; 220 Ω = 1.397 volts
VR2 = IR2 &acute; R2 (Ohm' s Law)
VR2 = 6.349 mA &acute; 470 Ω = 2.984 volts
VR3 = IR3 &acute; R3 (Ohm' s Law)
V
I
R
VR3 = 6.349 mA &acute; 1.2 K Ω = 7.619 volts
21
Example: Series Circuit
Solution:
Verify Kirchhoff’s Voltage Law:
VT = VR1 + VR2 + VR3
12 v = 1.397 v + 2.984 v + 7.619 v
12 v = 12 v
Another way to view series circuit total as resistance is to
transform individual resistance into an equivalent resistance.
Becomes
IT =
VT
RT
12 v
1.89 kW
I T = 6.349 mAmp
IT =
22
Parallel Circuits
Characteristics of a Parallel Circuit
• The voltage across every parallel component is equal.
• The total resistance (RT) is equal to the reciprocal of the sum of the
reciprocal: 1 1 1
1
1
RT
=
R1
+
R2
+
R3
RT =
1
1
1
+
+
R1 R 2 R 3
• The sum of all of the currents in each branch (IR1 + IR2 + IR3) is equal
to the total current (IT). This is called Kirchhoff’s Current Law.
IT
+
+
VR1
VT
VR2
-
-
+
+
VR3
-
-
23
RT
Example: Parallel Circuit
Example:
For the parallel circuit shown, use the laws of circuit theory to calculate
the following:
• The total resistance (RT)
• The voltage across each component (VT, VR1, VR2, and VR3)
• The current flowing through each component (IT, IR1, IR2, and IR3)
• Use the results to verify Kirchhoff’s Current Law.
IT
IR1
IR2
+
+
VR1
VT
+
VR2
-
-
IR3
+
VR3
-
-
24
RT
24
Example: Parallel Circuit
Solution:
Total Resistance:
RT =
1
1
1
1
+
+
R1 R 2 R 3
1
1
1
1
+
+
470 W 2.2 kW 3.3 kW
R T = 346.59 W
RT =
Voltage Across Each Component:
Since this is a parallel circuit :
VT = VR1 = VR2 = VR3 = 15 volts
25
Example: Parallel Circuit
Solution:
Current Through Each Component:
VR1
IR1 =
(Ohm' s Law)
R1
V
15 v
IR1 = R1 =
= 31.915 mAmps
R1 470 W
V
15 v
IR2 = R2 =
= 6.818 mAmps
R2 2.2 k W
IR3 =
IT =
V
I
R
VR3
15 v
=
= 4.545 mAmp
R3 3.3 k W
VT
15 v
=
= 43.278 mAmp
RT
346.59 W
26
Example: Parallel Circuit
Solution:
Verify Kirchhoff’s Current Law:
IT = IR1 + IR2 + IR3
43.278 mAmps = 31.915 mA + 6.818 mA + 4.545 mA
43.278 mAmps = 43.278 mAmps
Another way to view parallel circuit total as resistance is to
transform individual resistance into an equivalent resistance
Becomes
IT =
VT
RT
15 v
346.59 W
I T = 43.278 mAmp
IT =
27
Summary of Kirchhoff’s Laws
Kirchhoff’s Voltage Law (KVL):
The sum of all of the voltage drops in a
series circuit equals the total applied
voltage.
Gustav Kirchhoff
1824–1887
German Physicist
Kirchhoff’s Current Law (KCL):
The total current in a parallel circuit equals
the sum of the individual branch currents.
28
Example: Combination Circuit
As an example of how a combination circuit can be thought of as
equivalent total resistance the sequence below shows how the
series and parallel parts of the circuit are reduced to an equivalent
total resistance.
Becomes
Becomes
IT =
VT
RT
Becomes
12 v
879.29 W
I T = 13.647 mAmp
IT =
29
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