Download Ohm`s Law Ohmic relationship –V=IR Non Ohmic devises Electric

Ohm’
s Law
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V/volts
I/amperes
R/ohms
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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
10 10 10 10 10 10 10 10 10 10
V = IR
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Slope = V/I = R
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I(A)
Non Ohmic devises
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The connection between voltage and resistance can be
more complicated in some materials. These materials are
called non-ohmic (e.g. semiconductor devices such as
transistors). We'll focus mainly on ohmic materials for
now, those obeying Ohm's Law. Semiconductors will be
covered later on.
Worked Example:what is the voltage across a resistor
of 1K5 when a current of 2mA flows?
V = IR = 1500*0.002 =0.2V = 200mV
Self Assessment Question: A copper wire has a length
of 160m and a diameter of 1mm. If the wire is connected
to a 1.5v battery, how much current flows through the
wire?
Electric Power
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Electric Power
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Worked Example: A current of 10mA flows
through a resistor when the potential difference
across it is 1.5V. How much power is dissipated
in the resistor.
P = VI = 10e-3*1.5 =15mw.
Self-assessment Question: If a light bulb
operating at full power of 100W has a potential
difference of 15V across it. What is the
resistance of the bulb.
Ans. 2R2
Power is the rate at which work is done. It has
units of Watts. 1W = 1J/s
Electric power is given by the equations:
P =VI.
Batteries and power supplies supply power to
a circuit, and this power is used up by anything
that has resistance.
The power dissipated in a resistor goes into
heating the resistor. In many cases, this is
wasted energy. In some cases, however, the
heating is exploited as a source of heat, such
as in a toaster or an electric heater.
P = I2R ( since V =IR)
Schematic representation
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Resistor
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Battery
Resistive circuit
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Prepared by Dr Yonas M Gebremichael, 2005
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Ohms law states that current through the
conductor is directly proportional to the
voltage across it if temperature and other
physical conditions do not change.
In many materials, the voltage and resistance
are connected by Ohm's Law:
Ohm's Law : V = IR
Conductors which obey Ohms law are made up
of metals, carbon and some alloys. They are
called ohmic conductors.
V(v)
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Ohmic relationship –V=IR
Series connection of resistors
Resistors in a circuit
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Series configuration
Equivalent resistance
Series connection of resistors
The arrow in the above circuit shows
direction of current flow, by convention
the arrow end is at the positive end.
 Thus the potential at the left end of
each resistor is more positive than at the
right, because the current is flowing
from left to right.
 In a series configuration, the same
current flows through each component
in the circuit.
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RT R1 R2 R3
Resistors in series
Resistors in series
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Thus we can calculate the
voltage drop (potential
difference) cross each resistor
using ohm’
s relationship.
V1=IR1,
V2=IR2,
V3=IR3
The total voltage drop across
all the resistors is V1+V2+V3
and this must be equal to the
applied e.m.f assuming ideal
source.
Hence
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What are the voltages across R1 and R2?
RT = R1+R2 = 15k
I = V/R = 30/15k = 2mA
Thus V1 = R1*I =10k*2mA =20v.
And V2 = R2*I = 5k*2mA =10v.
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Note that V1 + V2 = 20v+10v=30V.
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Vs V1 V2 V3
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Vs IR1 IR2 IR3
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Vs I (R1 R2 R3 )
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If
RT is the combinedresistance
Vs IRT
Worked Example:
IRT I (R1 R2 R3 )
Resistors in series
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Self-assessment question:
Three resistors R1, R2 & R3 of resistance values
100Ω, 200Ω, and 500Ωrespectively are connected in
series across a 10V e.m.f. source of negligible internal
resistance. By first drawing a schematic diagram of
the circuit, calculate (a) the equivalent resistance,
(b)the current flowing in the circuit, (c) the potential
difference across each resistor (d) the power
dissipated in each resistor and (e) the power taken
from the e.m.f. source.
Ans. a) 800Ω, b)12.5mA c)1.25V, 2.5V, 6.25V
d)15.6mw, 31.3mw, 78.1mw e)125mw.
Summary of resistors in series
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The resistance equivalent to ‘
n’number of
resistors connected in series is the sum of the
individual resistances.
Always check the equivalent resistance is
larger than every individual resistor value.
Same current flows through each resistor in
series.
The voltage drop across each series resistor is
proportional to its resistance.
The sum of all the voltage drops across all the
series resistors is equal to the source voltage.
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Prepared by Dr Yonas M Gebremichael, 2005
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Resistors in parallel
Resistors in parallel
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Note that the combined resistance is less that either resistance
Putting resistors in parallel provides alternative paths for the
current and lowers the effective resistance.
Worked Example: Two resistors
of values 10K and 20K are
connected in parallel across a
voltage of 5V. What is the value of
the currents flowing through each
resistor. Draw a fully labelled
schematic of the circuit.
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Resistors R1 and R2 are in
parallel
The same voltage acts across
each resistor
The total current I from the
supply equals the sum of the
separate currents I1 and I2
through each resistor.
Summary of resistors in parallel
Parallel network
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Self-assessment question.
In the circuit shown below, find the voltage drop across each
resistor. What single resistor would replace the network.
Ans. V1 = 11.88, V2 = 0.12V, V3 = 12V, 840K
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The current divider
The Voltage divider
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The potential divider arrangement provides convenient way of getting
a variable voltage from a fixed voltage supply. Consider two resistors
R1 and R2 connected across emf Vs. The voltage divider rule states
that the voltage Vs divides between R1 and R2 in the ration of their
resistances.
The resistance equivalent to ‘
n’number of resistors
connected in parallel is the inverse of the sum of the
reciprocals of the individual resistances.
Always check the equivalent resistance is smaller than
the smallest resistance value in the network.
The voltage across each resistor is the same for all
the resistors in the parallel network.
The current through each resistor in parallel is
inversely proportional to its resistance.
The sum of all the currents through each resistor is
equal to the total current drawn from the source.
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The current divider arrangement divides
the current between the resistor branches
in proportion to their conductance. In the
circuit shown I1 and I2 are divided in
proportion to the conductance of R1 and
R2.
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Prepared by Dr Yonas M Gebremichael, 2005
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Variable Resistors
Voltage and Current dividers
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Variable resistors also called pots
(short for potential divider).
Unlike the usual resistors (two
terminals), these devices have
three terminals.
Two end terminals are connected
and the centre connection, also
called wiper, moves the output
voltage of the pot from zero to
the value of the voltage supplied
across the ends of the whole
resistive track.
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Voltage and current dividers
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Self-assessment question: A 2.5k
linear pot is used as a potential divider
for a 9V supply as shown in the figure
below. The wiper is set at B 4/5 of the
way round from end C of the track.
 what is the resistance of the length
BC of the track?
 What is the voltage across BC.
 If a resistor is connected as a load
to X and Y, what does the voltage
become across BC when the load
resistance is (i) 10k (ii) 20k.
Comment on the results.
 Ans. 2k, 0.5k, 7.2V, (I) 7V (II) 6V
Measurement of R,I,V
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Voltmeters: to measure the
voltage across a circuit
component, the voltmeter is
connected across the component.
Voltmeter is connected in parallel.
Connecting the voltmeter across
R2 should not affect the the
quantity under measurement. In
this case the voltage drop across
R2 will not change by connecting
the Voltmeter so long as the
voltmeter does not draw any
current. Thus an ideal voltmeter
will have an infinite resistance!
Which measurement, V or I?
Measurement of V, I & R
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Measuring Current
To measure current, the circuit has to be broken and an
ammeter inserted in the path of the current to be measured.
Ammeter is connected in series.
Addition of the ammeter to the circuit should not change the
quantity to be measured, in this case current. Therefore an ideal
ammeter must have zero resistance so it does not drop and
voltage across it.
Worked Example:
A 20k linear pot is used as a potential divider for a 9V supply. If the wiper is
set halfway round the track, what is the voltage when the load resistance is:
 A. very large
 B 100K
 C. 10K
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Which measurement technique do you think will be the more
useful?
Voltage measurements are used much more often than current
measurements.
The processing of electronic signals is usually thought of in voltage
terms.
It is an added advantage that a voltage measurement is easier to make.
The original circuit does not need to be changed. Often, the meter
probes are connected simply by touching them to the points of interest.
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Prepared by Dr Yonas M Gebremichael, 2005
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Ohm meter: measures resistance.
Ohmmeters work by passing a small current through the component and
measuring the voltage produced.
An ohmmeter does not function with a circuit connected to a power supply. If you
want to measure the resistance of a particular component, you must take it out
of the circuit altogether and test it separately.
If you try this with the component connected into a circuit with a power supply,
the most likely result is that the meter will be damaged. Most multimeters have a
fuse to help protect against misuse. The reading will not be accurate.
Measuring V, I & R
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Multimeter
A multimeter is a general purpose
electrical measuring instrument which is
capable of measuring current and voltage
(a.c. and d.c.) and resistance. It has
several ranges for each of these
quantities. Each range has a different full
scale value which can be set by switches.
Modern multimeters have auto ranging
capability.
 Moving coil multimeter: displays the
quantity as a mechanical deflection of
the pointer across a graduated scale.
 Digital multimeter displays the
measured value as a decimal digit.
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Prepared by Dr Yonas M Gebremichael, 2005
Measuring V, I & R