Question

The maximum resistance of a network of five identical resistors of $\frac{1}{5}$ $\Omega$ each can be –

• A. 1 $\Omega$
• B. 0.5 $\Omega$
• C. 0.25 $\Omega$
• D. 0.1 $\Omega$

Answer 1

The Correct Option is A

Step 1: Problem Definition:
We are provided with five identical resistors, each possessing a resistance of \( \frac{1}{5} \, \Omega \). The objective is to ascertain the maximum possible resistance of the network constructed from these five resistors.

Step 2: Maximum Resistance Principle:
The highest resistance in a resistor network is achieved when all resistors are connected in series. In a series configuration, the total resistance \( R_{\text{total}} \) is the aggregate of the individual resistances.

Step 3: Series Connection Formula:
The total resistance for resistors in series is calculated using the formula: \[R_{\text{total}} = R_1 + R_2 + R_3 + \dots + R_n\] where \( R_1, R_2, R_3, \dots, R_n \) represent the resistances of the individual resistors.
Given that all five resistors are identical with a resistance of \( \frac{1}{5} \, \Omega \), the calculation is: \[R_{\text{total}} = 5 \times \frac{1}{5} = 1 \, \Omega\]

Step 4: Conclusion:
The maximum resistance attainable by the network of five resistors is \( 1 \, \Omega \), realized when all are arranged in series.

Correct Answer: 1 \( \Omega \)