Download What is the current, I?

Electric Charge
One of the seven fundamental SI units.
Circuit analysis involves determining the current flowing
through and the voltage present across circuit elements.
Current and voltage are both based on electric charge.
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Electric Charge
In the early 1900s, scientists began to identify the
particles that make up atoms (subatomic particles).
They identified the proton, the neutron, and the
electron.
2
Electric Charge
Protons (positive charge) and neutrons (neutral or
no charge) are bound in the nucleus and do not
affect electrical behavior.
3
Electric Charge
Electrons (negative charge) surround the nucleus
occupying specific energy states.
Their exact
position is unknown, but their energy level is
precisely known.
4
Electric Charge
When an electron is removed from its atomic
orbital, it becomes a free electron. The flow of free
electrons (negative charges) or the “flow” of the
“holes” left in the orbitals after the electrons leave
(positive charges) constitute an electric current.
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Electric Charge
Charge is responsible for electrical forces.
Charge must be conserved – it cannot be created or
destroyed.
Charge is measured in coulombs (C) and is
abbreviated “q”.
The charge of one electron is –1.602  10-19 C.
–1 C
equals the charge of 6.24  1018 electrons.
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Current
Electric current is the flow of electric charge.
Current is measures in amperes (A) and is
abbreviated with the symbol “I” or “i”.
“Amperes” is often shortened to “amps”.
NOTE: A meter that measures current is called an
“ammeter” – NOT an “ampmeter”!
1 A = 1 C/s
dq( t )
i( t ) 
dt
f
q( t )   i( t ) dt
i
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Current
dq
i=
dt
t
q(t) = ò i(t)dt + q(t0 )
where t0 is some initial time at which the charge is known.
to
Voltage
Voltage is the difference in electric potential
between two points.
Voltage provides an electromotive force – a force
that moves charge carriers through a circuit.
Voltage is measured in volts (V) and is abbreviated
with the symbol “V” or “v” (or sometimes “E” ).
NOTE: A meter that measures voltage IS called an
“voltmeter”!
One joule of energy is needed to move one coulomb
of charge through a potential difference of one volt.
1 V = 1 J/C
(1 J = 1 kg-m2/s2)
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Voltage
I
V
+
-
Voltages can be constant with time or they can vary.
V
I
Constant Voltage : DC voltages
V(t) = 10 V
I
V
Varying Voltage in time and magnitude: AC voltages
V(t) = 10 cos (200πt)
VMsinωt
VM
0
VMcosωt
π/2
π
2π
3π
4π
ωt
Basic Circuit Elements
• Sources (voltage and current)
– Independent sources
– Dependent sources
• Resistors
• Capacitors
• Inductors
CIRCUIT COMPONENTS
•
•
•
•
•
•
v5
v3
v2
i7
i1
i6
v6
•
•
i2
v1
•
•
BRANCH:
a single path in a circuit composed of one
simple element and the nodes at either
end of the element
NODE:
a point at which two or more elements
have a common connection
SUPERNODE:
a closed surface containing several nodes
MESH:
a loop that does not enclose another loop
SUPERMESH:
a closed path around adjacent meshes
that share a current source
CLOSED PATH (OR A LOOP):
a closed path through circuit components
v4
•
•
i3
i4
Simple Circuit Laws
• Ohm’s Law
• Kirchhoff’s Current Law (KCL)
• Kirchhoff’s Voltage Law (KVL)
Ohm’s Law
Shows a linear relationship
between voltage and current.
V = IR, where V=voltage,
I=current, and R=resistance
Interpretation (DC circuit): The
voltage across a circuit element
is directly proportional to the
current through the element.
The proportionality constant is
called the “ resistance ” of the
circuit element.
Linear Relationship:
V = R I ↔ y = mx + b
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Ohm’s Law
•The two extreme values a resistor can take are zero
(short-circuit) and infinity (open-circuit):
•SHORT CIRCUIT:
defined as a “zero resistance
element”; i.e. an ideal wire.
•OPEN CIRCUIT:
defined as an “infinite
resistance element”; or an “open” path in a circuit.
•In a basic circuit all wires will be assumed to have
zero resistance. In practical applications, the
resistance of wires may have to be taken into account.
•Real resistors have certain limitations; the most
common one is a “power” rating: i.e. resistors can
only support a certain amount of electrical power (vi)
before failing.
R
vR
+
iR
v R = iR × R
MEASURING V & I
• Voltage is measured ACROSS a device; the probes of a voltmeter
are attached at both ends of the device under test or in parallel
with device.
• Current is measured THROUGH a device; the ammeter must be
connected in series with the device
What is the current, I?
Gustav Kirchhoff
Node: A closed path enclosing
part of a circuit.
Kirchhoff’s Current Law (KCL)
The sum of the currents entering
a node equals the sum of the
currents exiting that node.
A violation of KCL violates
the Law of Conservation
of Charge (or Mass)!
In other words: Whatever
goes in must come out.
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Gustav Kirchhoff
Kirchhoff’s Voltage Law (KVL)
The sum of the voltage rises
around any closed path in a
circuit equals the sum of the
voltage drops around that path.
A violation of KVL violates
the Law of Conservation
of Energy!
In other words: When you
make a round trip, you
end up where you started.
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Series and Parallel
Two or more circuit elements in series carry the same current.
Two or more circuit elements in parallel have the same voltage
across them.
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Series and Parallel
Series: Two or
more
circuit
elements carry
same current.
Parallel: Two or
more
circuit
elements have
the
same
voltage across
them.
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Applications of KCL
22
Applications of KVL
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