Transcript Resistor - eLisa UGM

Electricity and circuit
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Electric Charge
• Ordinary matter is made
up of atoms which have
positively charged nuclei
and negatively charged
electrons surrounding
them.
• The unit of electric
charge is the coulomb
• Charge is quantized as a
multiple of the electron
or proton charge:
Helium atom (schematic)
Showing two protons (red), two neutrons (green)
and two electrons (yellow).
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Potential Difference and Electric
Current
• Charges can “lose” potential energy by moving from a
location at high potential (voltage) to a location at low
potential.
• Charges will continue to move as long as the potential
difference (voltage) is maintained.
• A sustained flow of electric charge due to the potential
difference is called an electric current.
• If 1 Coulomb of charge (6.25 x 1018 electrons) pass a
point each second, the current is 1 Ampere.
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Current …
• Electric current (I): the
number of coulombs of charge
that pass by a certain point per
second.
• Currents flow through metal
wires via the motion of
electrons, which are negatively
charged, BUT the direction of
motion of the electrons in a
circuit is always opposite to
the direction of the current.
When charged particles are
exchanged between regions
of space A and B, the
electric current flowing
from A to B is defined as
q
I
t
where Δq is the change in the
total charge of region B over a
period
of time Δt.
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Ions moving across a cell membrane
• The figure shows ions, labeled with their
charges, moving in or out through the
membranes of three cells. If the ions all cross
the membranes during the same interval of
time, how would the currents into the cells
compare with each other? Assuming that the
rate of flow is constant
– Cell A has positive current going into it because
its charge is increased, i.e. has a positive value
of q.
– Cell B has the same current as cell A, because
by losing one unit of negative charge it also
ends up increasing its own total charge by one
unit.
– Cell C’s total charge is reduced by three units,
so it has a large negative current going into it.
– Cell D loses one unit of charge, so it has a small
negative current into it.
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Current…
• In most DC electric circuits, it can be assumed that the
resistance to current flow is a constant so that the current
in the circuit is related to voltage and resistance by
Ohm's law.
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Number of electrons flowing
through a light bulb
• If a light bulb has 1.0 A flowing through it, how many
electrons will pass through the filament in 1.0 s?
– We are only calculating the number of electrons that flow, so
we can ignore the positive and negative signs. Also, since the
rate of flow is constant, we may use the definition of current
as Δq/Δt .
– Solving for Δq = I Δt gives a charge of 1.0 C flowing in this
time interval.
– The number of electrons is
• number of electrons
•
•
•
= coulombs ×electrons/coulomb
= coulombs/coulombs/electron
= 1.0 C/e
= 6.2 × 1018
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Problem #1
• Let’s consider what happens when the
nerve is stimulated to transmit information.
• When the blob at the top (the cell body) is
stimulated, it causes Na+ ions to rush into
the top of the tail (axon). This electrical
pulse will then travel down the axon, like a
flame burning down from the end of a fuse,
with the Na+ ions at each point first going
out and then coming back in. If 1010 Na+
ions cross the cell membrane in 0.5 ms,
what amount of current is created?
• note: this mechanism is adopted to be a
taste sensor
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Electrical
Resistance
• Most materials
offer some
resistance to the
flow of electric
charges through
them.
– This is called
electrical
resistance.
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Resistor…
• A resistor is a two-terminal
electrical or electronic component
that resists an electric current by
producing a voltage drop between
its terminals in accordance with
Ohm's law.
– The electrical resistance is equal to the
voltage drop across the resistor divided
by the current that is flowing through
the resistor.
• Resistors are used as part of
electrical networks and electronic
circuits.
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Resistance…
• Resistance (R) of a conductor depends on:
– Material (resistivity )
– Length (L)- longer conductors have more
resistance.
– Cross section (A)- thick wires have less
resistance than thin wires
– Temperature - higher temperature means more
resistance for most conductors
L
R
A
gold = 2.24x10-8Ωm
aluminium = 2.65x10-8Ωm
nichrome = 100x10-8Ωm
The resistance of fig 2 will be greater than that of fig 1
Object fig 3 will have a smaller resistance than fig 1
because the charged particles have less of it to get
through. How about figure 4?
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Resistor
• Resistor is simply a cylinder of ohmic
material with wires attached to the
end or by the symbol:
• Symbol of resistor:
Resistor
Variable
Resistor
Resistor symbols (US and Japan)
Resistor
Variable
resistor
Resistor symbols (Europe)
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Ohm’s Law
• For many conductors,
current depends on:
R
V
I
– Voltage - more voltage,
more current
• Current is proportional to
voltage
– Resistance - more
resistance, less current
• Current is inversely
proportional to resistance
V
I R
Calculate the value of R from this graph
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Example: resistor versus organic
semiconductor thin film
Kuwat Triyana et al., Current-Voltage Characteristics of Organic Semiconducting Copper– Phthalocyanine Deposited on an Interdigitated Au
Electrode, (Indonesian Journal of Chemistry, 2006).
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Voltage…
• Voltage is electric potential energy per unit charge,
measured in joules per coulomb ( = volts).
• It is often referred to as "electric potential", which then
must be distinguished from electric potential energy by
noting that the "potential" is a "per-unit-charge"
quantity.
• Like mechanical potential energy, the zero of potential
can be chosen at any point, so the difference in voltage
is the quantity which is physically meaningful.
• The difference in voltage measured when moving from
point A to point B is equal to the work which would
have to be done, per unit charge, against the electric
field to move the charge from A to B.
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Voltage…
Used to
calculate
current in
Ohm's law.
Used to
express
conservation
of energy
around a circuit
in the voltage
law.
Used to
calculate the
potential from
a distribution
of charges.
Is generated by
moving a wire
in a magnetic
field.
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Series and parallel circuits
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DC Circuit
• The basic tools for solving D C circuit problems are
Ohm's Law, the power relationship, the voltage law, and
the current law.
• The following configurations are typical.
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Two Loop Circuits
• A circuit with two loops and two sources is involved enough to
illustrate circuit analysis techniques.
• It may be analyzed by direct application of the voltage law and
the current law, but some other approaches are also useful.
• Given the voltages, current analysis may be carried out by:
– Voltage and current laws
– Superposition theorem
– Thevenin's theorem
– Norton's theorem
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Kirchhoff’s Voltage Law
(KVL)
• The voltage changes around any closed loop must sum to zero.
Parallel:
VB= VR1= VR2
Series:
VB= VR1+ VR2
• No matter what path you take through an electric circuit, if you
return to your starting point you must measure the same voltage,
constraining the net change around the loop to be zero.
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Kirchhoff’s Current Law
(KCL)
• The electric current which flows into any junction in an electric
circuit is equal to the current which flows out.
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Multiple Sources
• Two Loop Circuits: A circuit with two loops and two sources is
involved enough to illustrate circuit analysis techniques.
• It may be analyzed by direct application of the voltage law and
the current law, but some other approaches are also useful, such
as: superposition theorem, Thevenin’s theorem or Norton’s
theorem.
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Superposition: Two Loop Problem
• To apply the superposition theorem to calculate the
current through resistor in the two loop circuit shown,
the individual current supplied by each battery is
calculated with the other battery replaced by a short
circuit.
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One Loop Circuit with
Two Voltage Sources
•
Using the following figure;
a. Find current flowing through the circuit and its direction
b. Calculate voltage difference between a and b
5Ω
+
3V
b
12 V
+ -
I
a
7Ω
a. Assume that the direction of current and loop is the
same.
From KVL:
ΣV + ΣIR = 0
-3 + 12 + I(5+7) = 0
Therefore, I = -9/12 = -0.75 A
It means that the current is opposite direction of loop
b. the voltage difference between point a and b:
Vab= -3 V + (-0.75 A)(5 Ω) = -6.75 V, or
Vab= -12 V - (-0.75 A)(7 Ω) = -6.75 V
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Two Loop Circuits with
Two Sources
•
Using the following figure, find current
flowing through each resistor
3Ω
A
4Ω
V2
2I1
A
I1
I2
10Ω
4Ω
V2
10Ω
+
+
30 V
3Ω
2I1
-
30 V
B
B
• Using KCL at point A: I1-I2+(2I1) = 0
• Using KVL: -30 + 3I1+4I2 = 0 (left loop), +10(2I1) - V2 + 4I2 = 0 (right loop)
• From three equations we can find:
I1 = 2 A and I2 = 6 A, V2 = 64 V
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Two Loop Circuits with
Three Sources
1Ω
I1
+
2V
1Ω
A
I2
4Ω
Loop 1
Loop 2
+
+
-
I3
- 4V
2Ω
B
-
2V
2Ω
• Using KVL of loop 1:
-2V+I1(1)-I2(4)+4V+I1(2)= 0
3I1 – 4I2 = -2
• Using KVL of loop 2:
-2V+I3(1)-I2(4)+4V+I3(2)= 0
3I3 – 4I2 = -2
• Using KCL at point A:
Therefore, what are: I1, I2 and I3?
I1 + I2 +I3 = 0
how about direction of current?
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