From the combination of resistors with resistance values and , which of the following combination is the best circuit to get an equivalent resistance of ?

- A
Option
- B
Option
- C
Option
- D
Option
From the combination of resistors with resistance values and , which of the following combination is the best circuit to get an equivalent resistance of ?

Option
Option
Option
Option
Correct answer:A
Standard Method
Given: and .
Find: Which circuit gives equivalent resistance .
From the solution, the correct selection is stated to be Option A. The required principle is combination of resistors in series and parallel.
For the first option, the top branch has and in series, and the bottom branch has and in series. Therefore,
and
These two branches are in parallel, so
Therefore, the circuit in Option A gives the required equivalent resistance of . The correct option is A.
Check using series-parallel formulas
Given: and .
Find: The option whose equivalent resistance is .
Use the standard formulas:
The solution explicitly states that the first option gives the desired equivalent resistance of and concludes, "Thus, the correct answer is (1)." This maps to A.
Treating the first circuit as if all four resistors are in one series chain is wrong because the diagram has two separate branches between the same terminals. First identify branch structure, then combine the branches in parallel.
Adding parallel resistances directly is wrong. For parallel branches, use either
or the two-branch product formula
R_{\text{eq}} = \frac{R_1R_2}{R_1+R_2} $$.Using the resistor values incorrectly by taking all of as parallel and then adding in series is wrong for this question because that is not the arrangement of the correct option. Always read the actual circuit diagram before calculating.
Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.