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: Understanding the problem:
We are given five identical resistors, each with a resistance of \( \frac{1}{5} \, \Omega \). The task is to determine the maximum possible resistance of the network formed by these five resistors.

Step 2: Concept of Maximum Resistance:
The maximum resistance in a resistor network occurs when all the resistors are connected in series. In a series connection, the total resistance \( R_{\text{total}} \) is simply the sum of the individual resistances.

Step 3: Formula for Series Connection:
For resistors in series, the total resistance is given by the formula: \[ R_{\text{total}} = R_1 + R_2 + R_3 + \dots + R_n \] Where \( R_1, R_2, R_3, \dots, R_n \) are the individual resistances of the resistors.
In this case, since all five resistors are identical and have a resistance of \( \frac{1}{5} \, \Omega \), we can write: \[ R_{\text{total}} = 5 \times \frac{1}{5} = 1 \, \Omega \]

Step 4: Conclusion:
The maximum resistance of the network formed by the five resistors is \( 1 \, \Omega \). This occurs when all the resistors are connected in series.

Correct Answer: 1 \( \Omega \)