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Information Report

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MIXED RESISTOR CIRCUITS
| CONCEPT OVERVIEW
The topic of RESITIVITY can be referenced on page 200 of the NCEES Supplied Reference Handbook, 9.3 Version for Computer Based Testing. Resistor circuits that combine series and parallel resistors networks together are generally known as RESISTOR COMBINATION or MIXED RESISTOR CIRCUITS. Many circuits have a combination of series and parallel resistors. Generally, the total resistance in a circuit like this is found by reducing the different series and parallel combinations step-by-step to end up with a single equivalent resistance for the circuit. The METHOD OF REDUCTION teaches us that if you begin to combine all series and parallel combinations you can often end up with one equivalent resistance across the source. Then you can calculate backward the current and work backward to find all voltages and current. General rules and guidelines for performing the METHOD OF REDUCTION to consolidate circuit elements and calculate equivalence for elements are below. Remember that these are just guidelines and there are numerous ways to solve these types of problems. 1.
Two (or more) resistors with their heads directly connected together and their tails directly connected together are in parallel. They can be reduced to one resistor using the equivalent resistance equation for resistors in parallel.
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2.
Two resistors connected together so that the tail of one is connected to the head of the next, with no other path for the current to take, are in series and can be reduced to one equivalent resistor. A key thing to remember is that for resistors in series, the
current
is the same for each resistor, and for resistors in parallel, the
voltage
is the same for each one. The properties of RESISTORS IN PARALLEL and RESISTORS IN SERIES can be referenced under the topic of RESISTORS IN SERIES AND PARALLEL on page 200 of the NCEES Supplied Reference Handbook, 9.3 Version for Computer Based Testing.
CONCEPT EXAMPLE:
In the following example calculate the total current (I
T
) taken from the 12 V voltage supply.
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SOLUTION:
The overall approach for a circuit like this is to identify which sets of resistors are in parallel and which are in series. With these relationships established, we can calculate equivalent resistances, and ultimately, a single total equivalent resistance for the circuit. Given our calculated equivalent resistance, we then use Ohm’s Law to calculate the total current in the circuit. The first step we will make is to take the two resistors, R
2
and R
3
that are in “SERIES” and calculate the equivalent resistance:
R
2
+R
3
=8
!
+4
!
=12
!
The formula for RESISTORS IN SERIES can be referenced under the topic of RESISTORS IN SERIES AND PARALLEL on page 200 of the NCEES Supplied Reference Handbook, 9.3 Version for Computer Based Testing. We can replace resistors R
2
and R
3
above with a single resistor of resistance value 12
!
as depicted below:
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Our circuit now has a single resistor R
A
in “PARALLEL” with the resistor R
4.
Using our resistors in parallel equation we can reduce this parallel combination to a single equivalent resistor value of
R
COMB
:
R
COMB
=
1R
A
+
1R
4
R
COMB
=
112
+
112
R
COMB
=
6
!
The formula for RESISTORS IN PARALLEL can be referenced under the topic of RESISTORS IN SERIES AND PARALLEL on page 200 of the NCEES Supplied Reference Handbook, 9.3 Version for Computer Based Testing.

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