In the diagram R_1 > R_2 > R_3. Rank the three resistors from least to greatest
ID: 1613516 • Letter: I
Question
In the diagram R_1 > R_2 > R_3. Rank the three resistors from least to greatest by the current through them. Answer ___ A) 1, 2, 3 B) 3, 2, 1 C) 1, 3, 2 D) 3, 1, 2 E) All are the same When resistors 1 and 2 are connected in series, the equivalent resistance is 20 Ohm. When they are connected in parallel, the equivalent resistance is 3.2 Ohm. The resistance of the two resisters are: Answer ____ a) 10 Ohm and 20 Ohm b) 12 Ohm and 8 Ohm c) 8 Ohm and 17 Ohm d) 16 Ohm and 4 Ohm e) 15 Ohm and 10 OhmExplanation / Answer
1)
The answer is E) all are the same
because resistors are said to be connected in “Series“, when they are daisy chained together in a single line. Since all the current flowing through the first resistor has no other way to go it must also pass through the second resistor and the third and so on. Then, resistors in series have a Common Current flowing through them as the current that flows through one resistor must also flow through the others as it can only take one path.
2)
(1) R1 R2 = 20
(2) R1*R2/(R1 R2) = 3.2
from(1);
(3) R2 = 20 - R1
substituting in (2);
R1*(20 - R1)/(R1 20 - R1) = 3.2
(20*R1 - R1^2)/(R1 20 - R1) = 3.2
(20*R1 - R1^2)/(20) = 3.2
20*R1 - R1^2 = 20*3.2
20*R1 - R1^2 = 64
R1^2 - 20*R1 +64 = 0
by quadratic formula;
R1 = 16
using (3);
R2 = 4
R1 = 16
R2 = 4
The answer is (d) 16 and 4 ohm.