EQUIVALENT RESISTOR – RESOLUTION
Entrance exam exercises with commented solutions on
Equivalent resistor
01- (UFB) In each of the associations below, calculate the resistance of the equivalent resistor between the specified points:
the) 
b) 
w) 
d) 
and) 
f) 
g) 
h) 
i) 
j) 
l) 
02-(UFMS-MS) In the electrical circuit below, determine the value of the equivalent resistance between points A and B.
03-(UEL-PR) Consider the circuit represented in the diagram below, where each resistance is worth 10Ω.
The equivalent resistance between terminals X and Y, in ohms, is equal to:
a) 10
b) 15
c) 30
d) 40
e) 90
04-(UFRJ-RJ) The smallest equivalent resistance of the following circuits is (consider that the resistances are all the same):
05-(FGV-SP) Thinking about how to use the huge stock of 20Ω and 5Ω resistors that were “stranded” in a factory warehouse, the engineer in charge determines that an association of equivalent value (between points A and B) be made to the resistor that would be needed to assemble a certain device.
The employee who was soldering the alternative circuit, absent-mindedly, changed the order of the resistors and a large batch of associations had to be discarded.
The correct resistances in each association should be: R 1 = 20Ω, R 2 = 20Ω and R 3 = 5Ω.
The resistors assembled incorrectly in each association were: R 1 = 5Ω, R 2 = 20Ω and R 3 = 20Ω.
Replacing the resistors resulted in a decrease in the desired resistance, in each combination, of:
a) 5 Ω
b) 9 Ω
c) 15 Ω
d) 24 Ω
e) 25 Ω
06-(MACKENZIE-SP) A box contains resistors connected to three terminals, as shown in the figure below.
The relationship between the equivalent resistances between points A and B and between points B and C (R AB /R BC ) is:
a) 4/3
b) 1
c) 1/2
d) 2/3
e) 2
07-(UNICAMP-SP) There are several equal resistors with resistance R= 1Ω.
a) Make a diagram showing the minimum number of resistors required and the way they should be combined to obtain an equivalent resistance of 1.5Ω.
b) Show the schematic of another available resistor combination that also has an equivalent resistance of 1.5Ω
08-(UFF-RJ) In the middle of the first half of the 19th century, Georg Simon Ohm formulated a law that relates three important quantities in the study of electricity: voltage (V), current intensity (i) and resistance (R). Based on this law, in order to
To check whether a given resistor was ohmic, a student reproduced Ohm’s experiment, obtaining the following graph:
A) Report whether the resistor used in the student’s experiment is ohmic and, if so, calculate the value of its resistance.
B) Consider this resistor subjected to a voltage of 9.0 volts, during a time interval of 5.0 minutes, and determine, in joules, the dissipated energy.
C) Repeating the experiment with several resistors, the student found a set of three identical ohmic resistors and associated them in two different ways, as shown in figure 1. The student then immersed each association in equal amounts of water and subjected their terminals (X and Y) to the same potential difference, keeping it constant.
In this case, identify the combination capable of heating the water more quickly. Justify your answer.
09-(CESGRANRIO-RJ) In the circuit below, it is known that the equivalent resistance between points A and B is 3Ω.
So, the resistance value R, in ohms, must be equal to:
10-(PUC-RJ) When resistors R 1 and R 2 are placed in series, they have an equivalent resistance of 6 Ω. When R 1 and R 2 are placed in parallel, the equivalent resistance drops to 4/3 Ω. The values of resistors R 1 and R 2 , respectively, are:
a) 5 Ω and 1 Ω
b) 3 Ω and 3 Ω
c) 4 Ω and 2 Ω
d) 6 Ω and 0 Ω
e) 0 Ω and 6 Ω
11-(PUC-MG) In the circuit in the figure below, it is CORRECT to state that the resistors :
a) R1, R2 and R5 are in series.
b) R1 and R2 are in series.
c) R4 and R5 are not in parallel.
d) R1 and R3 are in parallel.
12-(PUC-RJ) Three identical resistors of R = 30 Ω are connected in parallel with a 12 V battery. It can be stated that the equivalent resistance of the circuit is
a) Req = 10 Ω
b) Req = 20 Ω
c) Req = 30 Ω
d) Req = 40 Ω
e) Req = 60 Ω
13-(UNESP-SP) Current cars are equipped with a rear heated window to eliminate fogging on humid or rainy days. To do this, resistive strips installed on the inside of the window are connected to the vehicle’s electrical system, so that it can transform electrical energy into thermal energy. In one of the vehicles manufactured in the country, for example, these strips (resistors) are arranged in a similar way to the one shown in the figure.
Considering the resistances of strips 1,2,….,6 respectively as R 1 =R 2 =……,=R 6 =R, make a diagram of the association that corresponds to the arrangement of the strips in the figure and calculate the resistance of the equivalent resistor.
14-(UFRN-RN) A ring made from a homogeneous conductive wire has, between diametrically opposite points, a resistance R.
If we cut this ring into 4 equal parts, two by two, with the larger pieces being twice the length of the smaller pieces, and connect them as shown in the figure above, we can say that, between points A and B, the resistance will be:
15-(UFRRJ-RJ) The following figure shows a simple circuit that powers an electric shower C.
Among the following resistance systems, the one that will heat the water most quickly is:
16-(UFRJ-RJ) A circuit is formed by an ideal battery, which maintains a potential difference V at its terminals, an ideal ammeter A, a switch and three identical resistors, each with a resistance of R, arranged as shown in the figure. With the switch closed, the ammeter records the current I. With the switch open, the ammeter records the current I’:
a) Calculate the ratio I’/ I.
b) If these three resistors were used to heat water in an electric shower, indicate whether we would have hotter water with the switch open or closed. Justify your answer.
17-(UERJ-RJ) Consider the association of three resistors: A, B, and C. Their respective resistances are R A , R B , and R C , and R A > R B > R C .
The diagram that presents the greatest resistance between points P and M is shown in:
18-(UNESP-SP) An individual wants to make the central electric heater in his home heat the water in the tank in the shortest possible time. The heater has a resistor with resistance R. However, it has two more resistors exactly the same as the one installed in the heater and which can be used for this purpose. In order to achieve his objective, taking all precautions to avoid accidents, and considering that the resistances do not vary with the temperature, he must use the circuit
19-(UNESP-SP) As a consequence of the rapid development of electronic technology , it is now possible to carry out experiments in various areas of science using samples with dimensions of the order of nm (1 nm = 10 -9 m). New perspectives have been introduced and are being explored, such as investigations into the electrical properties of macromolecules and polymer chains, such as proteins.
Faced with this possibility, a researcher successfully verified his hypothesis that a certain protein, when stretched, satisfied Ohm’s law. After systematic measurements of its electrical resistance, he concluded that its value is R. Continuing his investigation, he divided this chain into two pieces, connecting them in parallel, and the effective resistance was measured to be 3R/16. Considering that the shorter piece has resistance R 1 and the longer piece has resistance R 2 , calculate these values expressed in terms of R.
20-(PUC-RJ) Two resistors R 1 = 1 Ω and R 2 = 2 Ω are connected to a 2 V battery. How should these two resistors be combined so that the power dissipated in the circuit is as low as possible?
a) The resistors must be placed in series, and the power dissipated will be 4/3 W.
b) The resistors must be placed in series, and the power dissipated will be 3/4 W.
c) The resistors can also be placed in series or parallel, and the power dissipated will be 1 W.
d) The resistors must be placed in parallel, and the dissipated power will be 4/3 W.
e) The resistors must be placed in parallel, and the dissipated power will be 3/4 W.
21-(CFT-MG) FIG. 1 represents an association of identical resistors and FIG. 2, a battery and connecting wires.
To obtain the highest value of electric current, the wires must be connected at the points
a) A and B.
b) A and D.
c) B and C.
d) C and D.
22-(PUC-RJ) Two electrical resistors, one of 2Ω and the other of 6Ω, must be connected to an ideal 12 V battery in an electrical circuit.
a) Determine how the resistors should be connected so that the power dissipated by the circuit is as low as possible.
b) Draw the circuit corresponding to the answer to item a.
c) Determine the voltage value to which the battery should be adjusted so that the power in the electrical circuit increases by 300%.
23-(ITA-SP) In the electrical circuit in the figure, the various elements have resistances R 1 , R 2 and R 3 as indicated.
Knowing that R 3 = R 1 / 2, for the equivalent resistance between points A and B of the association in the figure to be equal to 2 R 2 the ratio r = R 2 / R 1 must be
24-(ITA-SP) An electrical circuit is made up of an infinite number of identical resistors, as shown in the figure.
The resistance of each element is equal to R. The equivalent resistance between points A and B is:
a) infinite
b) R.(√3 – 1)
c) R√3
d) R.(1 – √3/3)
e) R(1 + √3)
25-(UECE-CE) A long underground cable of 10 km extends from east to west and consists of two parallel wires of 13Ω/km. An improper contact is formed at a distance x, measured from the west end, when a conductive path of resistance R makes the connection between the wires, as shown in the figure.
The resistance is R=60Ω when measured from the western ends and 216Ω when measured from the eastern ends. The value of x, in kilometers is:
26-(UECE-CE)
The equivalent resistance R, between points P and Q, in ohms, of the combination of resistors shown in the figure is:
a) 0.15
b) 6.67
c) 9.33
d) 15.00
e) 22.5
27-(PUC-PR) The agricultural sector has undergone major transformations in recent years. Nowadays, rural properties are equipped with a good level of comfort, which was previously a privilege only for urban dwellers. Without a doubt, electricity is the main factor responsible for this modernization.
It allows for everything from the installation of electric motors, which increase the farm’s production capacity, to efficient lighting as well as the use of communication devices, such as radio, telephone, TV and many others, providing a better quality of life and reducing rural exodus.
In this way, the construction of small-scale plants can be an alternative for supplying electricity to small rural properties.
On farms, for example, it is common to use egg incubators. A standard egg incubator requires four 40 W – 120 V lamps to heat the internal environment.
These lamps must be left on 24 hours a day.
According to the text, select the CORRECT alternative.
a) Using the hydroelectric plant and assuming that the incubator lamps are connected in parallel, it is possible to supply electricity to 150 incubators per day.
b) In the table above, the generation capacity is related to the electrical power generated in each type of plant.
c) In the wind farm, the energy is non-renewable.
d) Assuming that the voltage remains constant in the association of the incubator lamps, the total power will be the same regardless of whether the connection is in series or parallel.
e) Assuming that the electrical voltage generated from photovoltaic panels is continuous and equal to 220 V, if we connect the incubator lamps in series, at this voltage they will work normally.
28-(UFB) Calculate in each case the resistance of the equivalent resistor between points P and Q:
the)
b)
w)
29-(UFV-MG) A circuit with three resistors is represented in the following figure.
A circuit with three resistors is represented in the following figure.
The resistance measured between points A and B is:
a) 6.0 Ω
b) 5.0 Ω
c) 2.2 Ω
d) 1.8 Ω
e) 1.2 Ω
30-(FUVEST-SP) A special conductive material becomes luminous when an electric current passes through it. Words were written on this material, and voltage sources were connected to terminals 1 and 2 in a dark room. The readable word is:
31-(PUC-SP) Determine the value of the equivalent resistance in the resistor association shown below:
32-(FUVEST-SP) Consider a circuit formed by 4 equal resistors, interconnected by perfectly conductive wires. Each resistor has resistance R and occupies one of the edges of a cube, as shown in the figure.
Applying a potential difference U between points A and B, the current that will circulate between A and B will be:
a) 4U/R
b) 2U/R
c) U/R
d) U/2R
e) U/4R
33-(MACKENZIE-SP) The resistance of the resistor equivalent to the association below, between terminals A and B, is:
34-(UFB) Determine the equivalent resistance in each of the associations below, between the specified points:
the) 
b) 
w) 
35-(FGV-SP) Determine the resistance of the equivalent resistor of the association below, between points x and y:
36-(UEL-PR) In the electrical circuit, represented below, the five resistors have the same electrical resistance R. Calculate the resistance of the equivalent resistor.
37-(MACKENZIE-SP) The electrical resistance of the resistor equivalent to the association below, between points A and B, is:
a) zero
b) 5.0 Ω
c) 10 Ω
d) 60 Ω
e) 135 Ω
38-(UF-PE) In the circuit, what is the equivalent resistance between points A and B?
39-(UECE-CE) Consider the following figure. It is formed by a set of resistors all with resistance R.
The equivalent resistance between points A and B is:
40-(PUC-SP) For the circuit below, consider that all resistors are ohmic and of electrical resistance R.
Calculate the value of the equivalent electrical resistance of the association.
41-(FGV-SP) After reading an article about the geometry and formation of fractals, a radio and TV technician decided to apply the theory to associations with resistors of the same value R . To start his fractal, he determined that the first cell would be the one drawn below: Then, he evolved his fractal, replacing each resistor with a cell identical to the original. He continued the evolution until reaching the given configuration:
The resistor equivalent to this arrangement has a value:
a) 3.375R
b) 3,250R
c) 3.125R
d) 3,000R
e) 2.875R
42-(UERJ-RJ) Observe the representation of the section of an electrical circuit between points X and Y, containing three resistors whose resistances measure, in ohms, a, b and c.
Assume that the sequence (a, b, c) is a geometric progression with a ratio of 1/2 and that the equivalent resistance between X and Y measures
2.0 W.
The value, in ohms, of (a + b + c) is equal to:
a) 21.0
b) 22.5
c) 24.0
d) 24.5
43-(PUC-RJ) Calculate the resistance of the circuit formed by 10 resistors of 10 kW, all placed in parallel with each other, and in series with 2 resistors of 2 kW, placed in parallel.
a) 1 kW
b) 2 kW
c) 5 kW
d) 7 kW
e) 9 kW
44 – (IME-RJ)
Knowing that all resistors in the infinite loop in the figure have resistance R, the equivalent resistance between A and B is:
a) R(1 + √2)/2
b) R(1 + √3)/2
c) 3R/2
d) R(1 + √5)/2
e) R(1 + √6)/2
45-(UESPI-PI)
The equivalent resistance between terminals A and B of the ideal battery in the following electrical circuit is equal to:
46-(MACKENZIE-SP) The electrical resistance of the equivalent resistor of
association below, between points A and B, is:
a) 2 R
b) R
c) R/2
d) R/ 3
e) R/ 4
47-(UFMS-MS)
Equal electrical resistances (each with a value of 12 Ω) connect the vertices A, B and C of a triangle, as shown in the figure.
Regarding equivalent electrical resistance, it is correct to state that,
a) between vertices A and B, is 12 Ω
b) between vertices B and C, is 8Ω
c) between vertices A and C, is 36 Ω
d) between vertices A and B, is 24 Ω
e) between vertices A and B, is 36 Ω
48-(CEFET-MG) Two resistors of 2.0 Ω and 4.0 Ω are connected in series and then the set is connected in parallel to a 12 Ω resistor . The equivalent resistance of this combination, in Ω, is
a) 2.0.
b) 4.0.
c) 8.0.
d) 12.
e) 16.