Electric Circuits
Lecture 2:
Sources and Resistances
By Sheharyar Zahid
More on series resistances
• Keeping KVL in mind, it states that the voltage rise must equal
the sum of the drops in the following circuit
[1]
Parallel Resistances
• For the Case of parallel resistances, we already know
• Now for this special case of two parallel resistances we can
also use the following formula to make our analysis easier
[1]
Parallel Resistances
• If we do a simple calculation we will see that the overall
resistance is decreased
• This is because now current has more paths to flow through
• Also note that if one of the resistances is much larger then it
can be ignored as the formula will show you
Potentiometer
• Consider a resistor that has a linear response
• The resistance can be varied if we change ‘l’ - the length of
the resistive element (recall the expression for resistivity)
• Such a device which can be made to vary its resistance by the
use of its ‘l’ along with a metal contact is called a
potentiometer
• Essentially it is just a ‘variable’ resistance
Various symbol conventions
for a potentiometer are
displayed
>>>
[1]
Voltage Divider
• A voltage divider does just that, it divides the voltage
• Function of this circuit is to take an input voltage (Vi) and
provide a scaled down output voltage (Vo), since we know
how the series resistance drops voltage we can say (Pg. 65)
[1]
Voltage Divider
• Also called voltage attenuator as we can see this is used to
drop the voltage hence attenuate it
• A two resistor voltage divider requires that the resistances be
in series (i.e. carry the same current) and share a simple node
• If any other elements are connected to the shared node then
we can no longer apply the given voltage divider formula
• Vo preserves the nature of Vi, i.e. AC will output AC and DC
will output DC
• Vo is also (theoretically) linearly proportional to Vi
• Try an example from Franco pg. 66
Voltage Gain
• A relationship can be established between the output and
input,
[1]
• We can see that the gain depends on the ratio of the resistors
• The choice of resistors will effect current and the power
absorbed by the divider
Variable gain attenuator
• Incorporating a potentiometer we can devise a variable gain
attenuator
[1]
• Can be used to control the volume of audio devices
Current Divider
• Produces an output current in response to an input current
[1]
• R1 and R2 share the same node therefore they are in parallel
and have a common voltage drop. The current divides in the
two resistances in an inversely proportional manner.
Current gain
• We can also find the current gain of the divider by expressing the
equation as
[1]
• Output is a fraction of input and is proportional to it
• Current gain depends on the ratio’s of the resistances
• Equal resistances split current equally (but practically, two identical
resistors can not be the same, why?)
• The larger R2 is than R1, the lesser the output current will be and
vice versa, if R2 >> R1 then output current will tend to zero
Resistive Bridge
• Consists of 2 voltage dividers (also called
bridge arms) with a common source Vs
[1]
• Now using the voltage gain formula on
slide 8 we can derive an expression for output voltage
[1]
Try example on pg. 72 of Franco
[1]
More on the resistive bridge
• If the resistance ratios on each arm are identical
i.e.
[1]
• Then output voltage = zero and the bridge is balanced
• A Wheatstone bridge is a resistive bridge with a variable
resistance
• Used in null measurements when one resistance connected is
unknown. Measurement is taken when output goes to zero
[1]
Resistive Ladders
• Look at the ‘Resistive Ladder’ below
[1]
• Using the knowledge you already possess it can be seen
[1]
An R-2R Ladder
• If we take the resistive ladder and set resistances equal to R
and 2R, we get an R-2R ladder that gives progressively
diminishing (halving) current and voltage levels
[1]
Some Applications
• The Wheatstone bridge is used in
instrumentation applications
• The R-2R ladder is used for making DAC’s –
you will study about DAC’s and ADC’s in a later
course
Practical Voltage Source Model
• We have already discussed how practical voltage sources have
internal resistances
[1]
• V=Vs only when there is no current (i)
• The i-v characteristic can be modeled by
[1]
Practical Voltage Source Model
[1]
• It behaves like an ideal V source with a series resistance
• Compare this to the i-v characteristics of the ideal V source
Practical Current Source Model
• Similarly a practical current source will exhibit a similar
behavior
• The internal resistance is modeled as being in parallel because
of how current divides in parallel (no current will divide in
series)
[1]
…About the i-v graphs
• We are assuming something in these i-v
graphs, can you guess what it is?
[1]
• It has to do with the uniformity of the
gradients ….
The proportionality!
• For the voltage source we are assuming that
the drop in voltage is linearly proportional to
the load current
• For the current source we are assuming that
current falls linearly proportional to the load
voltage
Important Tasks!
• Do all the examples in the Franco book up till
page 88 and page 92-95. They are very easy
and you have studied everything you need for
it. Quizzes can happen anytime
• NEXT WEEK WE WILL BEGIN: CIRCUIT
ANALYSIS
References
[1]
Franco, S 1995, Electric circuit fundamentals, 2nd Edn, Saunders College
Publishing