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TRANSCRIPT
Electric Circuits 1
• Electric Current
• Resistance and Ohm’s Law
and resistivity
•Energy and Power in Electric
Circuits
• Resistors in Series and
Parallel
•Equivalent resistive circuits
1
INTRODUCTION: Electrical circuits are part of everyday human life.
e.g. Electric toasters, electric kettle, electric stoves
All electrical devices need electric current to operate.
In this section we study charges in motion called electric current.
What is an Electric Current?
Electric current is the rate at which electric charges move
through a wire or a conductor (flow of electric charges).
PARTICLE CHARGE MASS
Electron 1.6 10-19 C 9.11 10-31 kg
Proton 1.6 10-19 C 1.67 10-27 kg
Neutron No charge 1.67 10-27 kg
Structure of the atom:
-Protons and Neutrons fixed in the
Nucleus
-Electrons move in different energy
levels. Valence electrons are free to
move
2
Electronic Current
Conventional Current
Direction of
positive flow
Time interval
dt
t
dtIq
dt
dqI
0
S.I UNITS: Charge in Coulombs (C)
Time in Seconds (s)
Current in Amperes (A)
If a charge, dq, passes through a given cross-section of a
conductor in a time, dt, then a current, , is said to have passed,
where:
3
ELECTROMOTIVE FORCE (EMF)
Any device which causes Charge separation to occur is said to
be a source of electromotive force or EMF.
i.e. A battery with EMF, , provides energy to the charges to make
them move through a wire.
S.I unit: VOLT (V)
A battery that is disconnected from any circuit has an
electric potential difference between its terminals that is
called the electromotive force or EMF:
Remember – despite its name, the EMF is an electric
potential or voltage, not a force.
Electric circuit: A closed path through which charge can
flow, returning to its starting point, is called an electric
circuit. i.e. A closed path is required for current to flow. 4
A battery uses chemical reactions to produce a potential difference
between its terminals. It causes current to flow through the
flashlight bulb similar to the way the person lifting the water causes
the water to flow through the paddle wheel.
When the switch is closed , it provides a closed path for electric
charges to flow.
i.e. the battery sends out positive charges from the positive terminal
and accepts them at the negative terminal.
5
Electric Current
The direction of current flow – from the positive terminal
to the negative one – was decided before it was realized
that electrons are negatively charged. Therefore, current
flows around a circuit in the direction a positive charge
would move; electrons move the other way. However, this
does not matter in most circuits.
Conventional
current
Electronic current
Conventional current
always tries to flow from
the positive terminal to
the negative terminal of
the battery. The symbol
of the battery:
6
We use circuit symbols to make understanding of circuits easier.
Shown are some common circuit symbols:
7
Ammeter
Consider a circuit of battery connected to a light bulb
as shown:
A
Bulb I
If we measure the current with an ammeter we find that
it has same finite value everywhere in the circuit.
e.g. 1 A or 0.01 A
If another bulb is added to the circuit, current will be
different.
i.e. Something about the light bulb limits the size of
current flow in the circuit.
The light bulb has some Impedance 8
IMPEDANCE: What restricts the current flow?
As charges move through a material they experience some
opposition to their flow. The degree of difficulty of current flow is
measured in terms of the Impedance of the material.
If a current I flows through a material
when an EMF, , is applied to the ends of
the material, then the material has an
Impedance, Z, given by: IZ
IZ
or
The S.I. Unit of Impedance is the Ohms
There are three basic circuit components which give rise to Impedance
For a pure resistive circuit: Z = R 9
RESISTANCE (R) Energy is dissipated in a
Resistor in the form of heat
CAPACITANCE (C) Energy is stored in a Capacitor
in the form of an Electric field
INDUCTANCE (L) Energy is stored in an inductor
in the form of a Magnetic field
Resistance and Ohm’s Law
Under normal circumstances, wires present some resistance to the
motion of electrons. Ohm’s law relates the voltage to the current:
Be careful – Ohm’s law is not a universal law and is
only useful for certain materials (which include most
metallic conductors).
Ohm’s Law: The current flowing through
a conductor is directly proportional to
the potential difference across the ends
of a conductor.
IRV
IV
IV
)constant(
IR OR
10
Linear Resistance
I
GradientR
1
εat
volt)at (
1
GradientR
Non-linear Resistance
I
R
IGradient
1
e.g. Thermistors, Diodes,
light bulbs 11
If the graph of current as a
function of applied EMF is Linear,
then the resistance is a constant.
Such conductors are said to obey
Ohm’s Law and are referred as
OHMIC
If the graph of current as a function
of applied EMF is non-linear, then
the resistance varies with the
applied EMF. Such resistors do not
obey Ohm’s Law (NON-OHMIC)
For such resistors, it is common to
define the dynamic resistance at
some desired EMF
Resistance and Ohm’s Law
Solving for the resistance from
Ohm’s Law, we find:
The units of resistance, volts per
ampere, are called Ohms:
Two wires of the same length and diameter will have
different resistances if they are made of different
materials.
This property of a material is called the resistivity, . The
resistance, R, of a wire of length, L, and cross-sectional
area, A, is given by:
IR
OR
12
Resistance and Ohm’s Law
The difference between
insulators, semiconductors,
and conductors can be clearly
seen in their resistivities:
13
Resistance and Ohm’s Law
In general, the resistance of materials goes up as the
temperature goes up, due to thermal effects. This
property can be used in design of thermometers.
Resistivity decreases as the temperature decreases,
but there is a certain class of materials called
superconductors in which the resistivity drops
suddenly to zero at a finite temperature, called the
critical temperature TC. e.g. Mercury 4.2 K,
Highest temperature at which Superconductivity has
been observed is 125 K.
14
Exercise 1: Suppose a charge of 20 C drifts through a conductor of
cross-sectional area, A, in 2.0 s. (i) Calculate the current through the
conductor, (ii) How many electrons will pass through this conductor
in 1.0 s to produce a current of 10A?
Exercise 2:
(i) How much current will flow through a lamp that has a resistance
of 60 when connected across a 12 V supply?
(ii) What is the resistance of an electric frying pan that draws 12 A
when connected to a 120 V circuit?
15
20 30
12
12 V
Exercise 3: For the circuit
shown, find the current
through and potential drop
(voltage) across each
resistor.
Energy and Power in Electric Circuits
Power is defined as the rate at
which the electrical energy is
converted to heat, P = dW/dt
The potential difference, V, between the ends of a wire is defined as
the work (potential energy), dw, required to move a charge , dq, from
one end of the wire to the other. i.e.
VdqdW
q
dW
q
dUV
Potential Difference = Work(Energy)/Charge
Idtdq
dt
dqI
Also, Current:
If this Power is supplied for a time, t, then the amount of Energy
converted to heat:
Energy = Power × Time
tR
VRtIVIttPE
22
S.I. Units: Energy (Joules), J S.I. Units: Power (Watts), W 16
R
VRIVI
dt
dqV
dt
Vdq
dt
dWP
22
Exercise 4: Calculate the power being
dissipated in each resistor in the circuit
Current flowing in the circuit:
A 4.050
20
R
VI
IRV
Power dissipated in the 10 : W6.1104.0 22 RIP
Power dissipated in the 40 : W4.6404.0 22 RIP
Total Power Dissipated: W8 4.66.1 TP 17
When the electric company sends you a bill, your usage is quoted
in kilowatt-hours (kWh). They are charging you for energy use, and
kWh is a measure of energy.
tPE
Resistors in Series and Parallel
18
Resistors connected end to end are said to be in series.
They can be replaced by a single equivalent resistance
without changing the current in the circuit.
In series circuit, same current flows through each resistor
21-4 Resistors in Series and Parallel
Since the current through the series resistors must be
the same in each, and the total potential difference is the
sum of the potential differences across each resistor,
...321 VVVV
We find that the equivalent resistance is:
321
321
RRRR
I
V
I
V
I
V
I
V
eq
19
Resistors in Series and Parallel
Resistors are in parallel when they are across the same potential
difference; they can again be replaced by a single equivalent
resistance:
20
21-4 Resistors in Series and Parallel Using the fact that the potential difference across each resistor
is the same, and the total current is the sum of the currents in
each resistor,
Note that this equation gives you the inverse of the resistance, not
the resistance itself!
...321 IIII
We find:
321
321
321
1111
...
RRRR
R
V
R
V
R
V
R
V
IIII
eq
eq
If just two resistors in parallel, then:
Sum
Product
21
21
RR
RRReq
21
Resistors in Series and Parallel
22
If a circuit is more complex, start with
combinations of resistors that are either purely
in series or in parallel.
Replace these with their equivalent resistances;
as you go on you will be able to replace more
and more of them.
EXAMPLE 1: Find the equivalent resistance between points A and B
Solution:
RCED = 4+ 2 = 6
RCD = 2
2
1
12
6
3
1
6
11
CDR
RAB = 8
23
EXAMPLE 2: Find the equivalent resistance between points A and B
of the circuit shown if each resistor is 2
Solution: To simplify the problem let us label
each resistor a, b, c, d, e, and f.
n.b. The resistors a and b are in series and
the combination is in parallel with resistor c.
The resultant of abc is in series with e.
a b
c
d e
f
x
y
z
u v Rxyz = 2+ 2 = 4
Rxz = 4×2/4+2 = 8/6
Rxzv = 8/6 + 2 = 20/6
Rxuv = 2 + 2 = 4
Rxv = (20/6 × 4)/((20/6)+ 4) = 1.8
24
25
Exercise 5: Consider the circuit shown with
three resistors, R1 = 250.0 , R2 = 150.0
and R3 = 350.0 connected in parallel to a
24.0 V battery. Find:
(i) the current supplied by the battery,
(ii) the current through each resistor.
Exercise 6: An electric heater draws a steady 15.0 A from a 120 V line.
(i) How much power does it require to operate? and
(ii) How much does it cost per month (30 days) if it operates for
3.0 hours per day and the electricity company charges 9.2 cents per
kWh?