Question

In which combination the four resistors be connected to have minimum resultant resistance?

• A. All of the resistors in parallel combination
• B. All of the resistors in series combination
• C. One in series with the parallel combination of other three
• D. Two resistors in series with the parallel combination of other two

Hint:

For minimizing resistance, use parallel combinations of resistors.

Answer 1

The Correct Option is A

To minimize the resultant resistance in a circuit, we need to use the property of resistances in parallel.
Step 1: Understanding the relationship for parallel resistors.
For resistors in parallel, the total (or equivalent) resistance \( R_{\text{eq}} \) is given by: \[ \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4} \] This means that when resistors are connected in parallel, their resultant resistance is always less than the smallest resistance in the combination. The more resistors you connect in parallel, the smaller the resultant resistance becomes.
Step 2: Comparing with other combinations.
- If all resistors are in series, the total resistance is the sum of the individual resistances, which results in a higher resistance compared to parallel connection.
- Combining some resistors in series and others in parallel will not yield the smallest resistance, as the series combination adds additional resistance.
Step 3: Conclusion.
Thus, to minimize the resultant resistance, all four resistors should be connected in parallel. The correct answer is (A).