Download ELECTRONICS 4 – Fundamentals of Electronics I

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El 04- Electronics 4
Laboratory Exercise 10 – Parallel Circuits, Part 1
OBJECTIVE: To determine the total resistance of several parallel circuits using one of
three formulas for calculations and to estimate the value prior to calculation. The
estimation and calculations will be verified with measurements.
MATERIALS: Protoboard; multimeter; resistors: 120 , 2.2K, 3.9K, 4.7K(2), 5.1K,
6.8K, 10K, 15K, 18K(4), 33K, 68K(2), 150K.
DISCUSSION: Resistors in parallel exhibit multiple current paths to the power supply.
As a result, the effective or total resistance that the power supply sees is less than the
value of any of the individual resistors. This provides us with some interesting circuitry
problems. Fortunately, there are several ways to work with parallel devices easily.
Our first rule for parallel resistors, again, is that the total resistance of the circuit will be
less than the value of the smallest resistor in the circuit. This is because in a parallel
circuit, we have multiple current paths. This allows more current to flow from the power
supply than would through the smallest resistor alone.
The second rule we can use takes advantage of the fact that resistors typically have
tolerances on their values, and may have real values that are as much as 10% above or
below the marked value of the device. As a rule of thumb, we can say that any resistor
that has a value greater than 20 times the value of the smallest resistor in parallel can be
ignored. This is because its value is so high compared to the others that it will have little
or no effect on the circuit. This assumes, of course, that we are willing to tolerate some
minor error in our design – not all systems would permit this.
To illustrate, suppose we have a 1K resistor in parallel with a 22K resistor. The total
resistance of the pair is about 956 , which is within the 5% tolerance of a gold-band 1K
resistor. So, the 22K resistor can be ignored in most cases.
We also have a quick method of estimating the value of two resistors in parallel. For
each resistor, divide its value by two. The estimated value of the pair is somewhere
between these two half-values. For example, suppose we have a 22K and a 33K in
parallel. One-half of 11K is 11K, and one-half of 33K is 16.5K. So, the value of the two
devices in parallel can be estimated to be between 11K and 16.5K. A good guess would
be 14K, about half-way between the two half-values. The actual value of a 22K and a
33K in parallel is 13.2K, so the 14K guess is pretty close.
There are three formulas that we can use to calculate the total resistance of two or more
resistors in parallel. The formula you choose depends upon how many devices you have
and whether they are of the same or different values. Use the formula that you feel best
matches the requirements.
Two resistors of equal value: If you have two resistors of equal value in parallel, simply
divide the value of one of the resistors by two. The total resistance will be equal to onehalf the resistors’ value. Similarly, if you have three resistors of equal value in parallel,
simply divide by 3.
Two resistors of unequal value: If you have two resistors of different values in parallel,
the easiest approach is to use the product-over-sum formula, RT = (R1 5 R2) / (R1 +
R2). Here, the total resistance of the two unequal resistors is equal to the product of the
their values divided by the sum of their values.
Many resistors of unequal values: In the case where you have more than two resistors
of unequal values in parallel, the easiest approach is to use the reciprocal of the sum of
the reciprocals formula. This is the same, in effect, as adding up the conductances of the
branches of the circuit. This formula appears as 1/RT = 1/R1 + 1/R2 + 1/R3 …, and can be
extended to any number of devices.
In this exercise, we are given a series of parallel resistor values. For each set of values,
we want first to estimate the approximate value of the total resistance of the set. We then
will calculate the actual resistance value using an appropriate formula. Finally, we build
the circuit and measure the actual value to see how close our estimates and computations
have been.
PROCEDURE:
1. Examine the chart below. Note that on the left, we have provided sets of resistors
that are assumed to be in parallel. We then provide a space where you can note
the smallest resistor that is within the set. Next, there is a space for your
approximation of the total resistance. Then, we provide a space for the calculated
value of the circuit, along with a hint as to which formula to use to make this
calculation. Finally, there is space for a measurement.
R1
R2
R3
R4
Smallest R
Estimate R
Formula
4.7K
4.7K
ER
6.8K
15K
PS
120
3.9K
PS
2.2K
68K
PS
4.7K
5.1K
PS
5.1K
6.8K
150K
RS
10K
33K
150K
RS
Calculated
Measure
6.8K
10K
33K
RS
18K
18K
18K
18K
ER
4.7K
4.7K
68K
68K
ER and PS
2. To fill in the chart, follow these steps for each row:
A. Examine the values given.
B. Select the smallest resistor of the given set, and write its value down in the
column marked Smallest R. This may provide you with information when
making your estimate.
C. Estimate the value of the total resistance of the given resistor set.
1. For two resistors of equal value, simply divide that value by two.
For three resistors, divide by three, etc..
2. For two resistors of unequal value, use the quick method
described in the discussion above.
3. For many resistors of unequal value, select the largest and the
smallest values. Then. use these with the quick method.
D. Next, calculate the actual value of the resistors in parallel. As a hint, we
have provided you with a key to the formula that should be used. The key
is ER for two resistors (or more) of equal value, PS for product-over-sum,
and RS for the reciprocal of the sum of the reciprocals approach.
E. Finally, build the circuit and measure the value to see how close your
estimate and calculations were to the real value.
3. When you have completed the measurements, return the equipment and supplies
to their normal storage areas. Then, answer the questions below in writing for
credit.
REVIEW QUESTIONS:
1. You are given resistors of the values 1K, 4.7K, 10K, and 20K all in parallel. The
total resistance of this group should be smaller than _____________?
2. Six 10K resistors are in parallel. Estimate the total resistance.
3. A 4.7K resistor and a 9.1K resistor are in parallel. Find the total resistance using
both the product-over-sum and reciprocal formulas. How do the two computations
compare?
4. What must be done to measure the resistance of only one resistor in a parallel
circuit?
5. Given a 1K resistor and a 68K resistor in parallel, estimate RT.