Download Resistors in Parallel

In this section, we will show you how these principles apply to actual
electronic components and which components are used to provide
current, voltage, capacitance, and resistance.
The Power Source
In making an electric circuit the first thing you will need is
electricity. If not, then it’s not electric, no electrons will flow, etc.
So you have to get, create, or innovate a power or an energy
source.
A power source could be a
 Battery
 Voltage regulated source
 Straight from the plug in your house
• The first two are direct current or DC sources while the last is
an alternating current or AC source.
DC Power Source
- Currents and voltage is supplied as a continuous or direct
signal.
- Can be represented as a straight horizontal line in either a
voltage or a current vs. time graph.
- DC voltages usually range from 1.5 V to 12 V for
household devices to as high as 24 to 28 V for industrial
machines.
- Since voltage is a potential difference, you must need to
indicate the polarity, where positive and the negative
sides are.
voltage
12 Volts
time
A 12-Volt DC Signal
AC Power Source
- Represented mathematically as a sine wave.
• The sine wave (hence, the current) alternates from
positive to negative hence the name alternating current.
• In the Philippines, the frequency of the waveform is 60
cycles per second or 60Hz in some countries, it is 50Hz.
• AC Voltages (represented by the amplitude of the sine
wave) usually are from 100 to 250V, divided into two
ranges, 100 to 120V (average 110V) used in many
western countries, and 220-240V (mostly220V) here in
the Philippines.
• In the Philippines, our AC Voltage rating is 220V, 60Hz.
What source to use?
You must know whether a device you will be using needs a DC
Source or an AC Source. Here are some tips:
1. Look at the labels of the device, you will see if it runs on AC,
DC or both AC and DC.
2. Another concern when selecting supplies is the maximum
current that the voltage source can supply.
Power Source Circuits
Figures below show the symbol for the most power (voltage)
sources and sample values of voltages.
Symbols for Some Power (Voltage) Sources
A battery is indicated by alternating short and long parallel lines.
Each pair of lines (ideally) indicates one cell of the battery: the
shorter line indicates the negative end of the battery, and the
longer the line indicates the positive end of the battery.
DC Voltage source just indicate the polarity while he Ac voltage
source is described by the sine wave.
When solving mathematically, we assume that these voltages can
supply an unlimited amount of current, unless indicated
otherwise.
The Load and Equivalent
Components
Loads –components that consume the power source
which is the component that supplies energy.
• Power source must be at least of enough value to
overcome the load.
One example of a load is a light bulb. If you take a look at a
40-watt bulb, you would see something like this: 220V, 40W.
What does 220V, 40 W on a light bulb mean?
220V means that this light (or load) needs a voltage source
with 220-volts. If it’s too low, it won’t work. If it’s too high, it
will destroy the bulb.
40W is the power consumption of the bulb. So in one hour,
this bulb will consume about 0.4 kilowatt-hour (kwh).
Fixed Resistors (Resistors)
-
Simply resistors
Are components that have a definite resistance.
Resistance is measured in ohms.
Resistor could have a resistance as low as 10 ohms (Ω) to
as high as 10,000,000 ohms (Ω)
- Also has a power rating
- Come in 1/4th watt, ½ watt and even 1-watt ratings
This means that the power dissipation is equal to that
amount
Why do we need a resistors, since this will just impede the flow
of current across a material? Here are the reasons.
1. Resistors are current limiters.
According to Ohms Law, i = V/R, so give n a fixed voltage
source, the current will be dependent on the resistance.
Some component have specified current ranges for it to work.
Low current, High resistance
Rmax = V/ imin = 5 V / 0.01 A
= 500 Ω
+
5 Volts
-
Components
High current, Low resistance
Rmin = V / imax = 5 V / 0.05 A
= 100 Ω
If a certain device A has a current range from 10mA (0.01 A)
to 50mA (0.05 A), then you must have a resistor present that
would produce a current that is equal to or less than 50mA,
which from figure above must be from 100 to 500 ohms.
If you use two rechargeable (NiCd) batteries (1.2 Volts
each) to power a small lighting device which operates from
30mA to 80mA of current, what range of resistor values
should you place in your circuit?
Given
Voltage sources
Minimum current
Maximum current
V
imin
imax
2.4 Volts (2 NiCd batteries)
30mA
50mA
Find: Range of resistor values (rmin, rmax)
Solution: Use Ohms Law to find the minimum and
maximum values.
High current, Low resistance
Rmin = V/imax = 2.4 V / 0.08 A
= 30 Ω
Low current, High resitance
Rmax = V/imin = 5 V / 0.03 A
= 167 Ω
So the range of resistors to use is from 30 ohms to 167 ohms
2. Resistors are current distributors.
“The greatest amount of current flows through the path with the
least amount of resistance.”
We have two lamps sharing one voltage source, the total current
determined by the resistor R.
Current is distributed evenly between L1 and L2
If two lamps are identical, then the current i due to the
resistor R will be distributed equally into the two lamps.
So,
V / R = i = i1 + i2
i1 = 0.5i and i2 = 5i
Both lamps will have the same brightness because they have
the same voltage and current.
How do we do is we want the first lamp to be brighter than
the second one?
We can place resistors together with the lamps, which will
determine how much current will pass through the lamps.
Resistors control the current passing through L1 and L2
The total current i is limited by the resistor R, given by
i = V/ R
The current i will then be distributed across the lamps i1 and
i2 where
i = i1 + i 2
We can apply Ohms Law for both lamps
i1 = V / 0.5R2
and
i2 = V / R2
Equating both equations through the voltage V and solving
for i1
0.5i1 R2 = i2 R2 therefore i1 = 2i2
So,
i = i1 + i2 = 2i2 + i2
i = i1 + i2 = i1 + 0.5i1
where i2 = (1/3) i
where i1 = (2/3) i
The current distribution will be as follows:
Lamp 1: 2/3 of the current
Lamp 2: 1/3 of the current
If the resistor beside lamp 1 is half that of the resistor
beside lamp 2.
The colors correspond to the values in the table below
Digits and Multiplier
Color
Code
Black
0
Brown
1
Red
2
Orange
3
Yellow
4
Green
5
Blue
6
Violet
7
Gray
8
White
9
Multiplier
Tolerance Codes
Color
Tolerance
No Band
20%
Silver Band
10%
Gold Band
5%
To memorize the sequence, the middle part is almost the
same as the colors of the rainbow except for Indigo.
Black Boy ROY G. BV Goes West, To No Silver and Gold
The first word Black is used just to indicate the first color, to
distinguish it from brown, which is the second color.
The word To indicates the start of the tolerance.
No means no Band.
Variable Resistors
-also common components as you can change their resistance
from zero to a given value, called its rating.
-for example a 100k Ω variable resistor means you can change
the resistance from 0 to 100k Ω.
-the value of a variable resistor is given as it’s highest
resistance value.
To change the resistance, some have a dial or a knob where
a turn corresponds to a change in resistance. These are
called Potentiometers.
In some devices, you need to turn a slot in the component to
change the resistance. These are called Trimmer resistors.
Volume controls are variable resistors. When you change
the volume you are changing the resistance, which changes
the current.
 Making the resistance higher will let less current flow so
the volume goes down.
 Making the resistance lower will let more current flow so
the volume goes up.
From the previous problem, it is said that if a certain device
A has a current range from 10mA (0.01 A) to 50mA (0.05 A)
and you have a 5 Volt source, then you must have a resistor
value which can be anywhere from 100 to 500 ohms.
Let us say that the device mentioned is a light source. If we
put 500-ohm resistor, then it will light dimly. If we place a
100-ohm resistor, it will shine the brightest. We could
improve that design using a variable resistor.
 We can use the resistor to make the light brighter or
dimmer.
1. Determine the lower limit of the resistance needed. This
will be the value of our fixed resistor.
In our circuit, we need to have at least 100-ohms or the
lamp will be damaged. So place a 100-ohm resistor in the
circuit.
2. The value of the potentiometer Rpot must be at least the
differences between the resistance values
Rpot =500 ohms – 100 ohms = 400 ohms
Adding a potentiometer, we can make the light source brighter or dimmer by
moving the knob.
Resistors in Series
A battery and three resistors connected together end to end,
forming a single line as shown
Resistors in Series
These would result in a current flow of only one path in the loop,
across each of the resistors, making them in series with each
other. Since the current flows only one path, then the amount of
current flowing across each resistor is the same.
For example if three resistors R1, R2, and R3 are in the series,
then the voltage across each resistor will be
V1 = i x R1
V2 = i x R2
V3 = i x R3
The total voyage across the three resistors will just be the same
as the voltage of the battery, thus..
V = V1 + V2 + V3
= i x R 1 + i x R2 + i x R 3
= i (R1 + R2 + R3)
This means the total resistance will just be
the sum of the individual resistances of the
resistors, so resistors in series have an
additive effect.
we can also substitute a single resistor having a resistance Req,
where
Req = R1 + R2 + R3
For any number of resistors n it will just be
Req = R1 + R2 + ……….. + Rn
Thus
V = i * Req
Req is termed as the equivalent resistance of the three
resistors in series. So when combining three resistors in
series, the result is a resistor with a bigger resistance.
Equivalent circuit of the three resistors
Series connections are used in many different ways. The
most familiar example is that type of Christmas tree light
set in which all bulbs go off if one burns out.
Resistors in Parallel
Let us now consider a battery and three resistors connected
together at the ends where one end of each is connected at point
A, with the other ends connected at point B.
Resistors in Parallel
The figure can be drawn in another way
Another way of representing resistors in parallel
In this set-up, we consider the component to be parallel to
each other. Since all are connected at the ends of the
battery, then they all have the same voltage, the same as
that of the battery. But then, the current that flows out of
the battery will be divided among the three resistors in the
circuit. So the current flow across each resistor will be given
by
The tool current across the three resistors will just be the
same as the current flowing out of the battery.
This equation means that the inverse of the total resistance
will just be the sum of the inverse of the individual resistances
of the resistors.
From Ohms Law that i = V/R. if we compare this with the
equation we just derived, we can get the following
relationship.
Cancelling out
V,
For n resistors it will just be
From this equation, a single resistor R can be substituted in
place of R1, R2 and R3. thus R in this equation is the equivalent
resistance of Req of resistors in parallel.
 Because of the inverse relationship, the equivalent resistance
Req is smaller that each of the resistance in the circuit.
Switches
-device that create a short circuit or an open circuit depending
on the position of the switch.
For a light, ON means short circuit. When the switch is OFF,
that means there is an open circuit.
When the switch is ON it looks and acts like a wire.
When the switch is OFF there is no connection.
The Minimum Circuit with a Switch
What is the current when the switch is off or open? When the
switch is on?
Answer
We won’t be needing the mathematical computations in this
example.
Switch Off
if the switch is off, then the circuit is “open”. Actually it is not a
circuit anymore because the circuit is a closed loop. Current
flows in a circuit. There is no current flowing if there is no
circuit, so i = 0 if the switch is of.
If the switch is on, the current will flow.