Four conductors of same resistance connected to form a square. If the resistance between diagonally opposite corners is `8 ohm`, the resistive between any two adjacent corners is

Options

A. 32 ohm
B. 8 ohm
C. `1/6` ohm
D. 6 ohm

Explanation

To solve the problem of finding the resistance between any two adjacent corners of a square formed by four conductors of the same resistance, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- We have a square formed by four resistors, each with resistance \( R \). The corners of the square are labeled A, B, C, and D.
- The resistors are connected as follows: AB, BC, CD, and DA.

2. **Resistance Between Diagonally Opposite Corners**:
- The resistance between corners A and C (diagonally opposite) is given as \( 8 \, \Omega \).
- When calculating the resistance between A and C, we can see that the path consists of two resistors in series (AB and CD) and two resistors in parallel (AD and BC).

3. **Calculating the Equivalent Resistance**:
- The total resistance \( R_{AC} \) can be expressed as:
\[ R_{AC} = \frac{R + R}{2} + R + \frac{R + R}{2} = 2R \]
- Since \( R_{AC} = 8 \, \Omega \), we have:
\[ 2R = 8 \implies R = 4 \, \Omega \]

4. **Finding Resistance Between Adjacent Corners**:
- Now, we need to find the resistance between two adjacent corners, say A and B.
- The resistors AB and AD are in series, while the resistors BC and CD are in parallel with respect to the path from A to B.

5. **Calculating the Resistance Between A and B**:
- The equivalent resistance \( R_{AB} \) can be calculated as:
\[ R_{AB} = R + \left( \frac{R \cdot R}{R + R} \right) \]
- Substituting \( R = 4 \, \Omega \):
\[ R_{AB} = 4 + \left( \frac{4 \cdot 4}{4 + 4} \right) = 4 + \left( \frac{16}{8} \right) = 4 + 2 = 6 \, \Omega \]

### Final Answer:
The resistance between any two adjacent corners is \( 6 \, \Omega \).