Four conductors of same resistance connected to form a square. If the resistance between diagonally opposite corners is 8 ohm, the resistance 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, we need to find the resistance between two adjacent corners of a square formed by four conductors of the same resistance. We know that the resistance between diagonally opposite corners is 8 ohms. Let's denote the resistance of each conductor as \( R \).

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- We have four resistors arranged in a square. Let's label the corners as A, B, C, and D.
- The resistors are as follows:
- AB = R
- BC = R
- CD = R
- DA = R

2. **Resistance Between Diagonal Corners**:
- The resistance between diagonally opposite corners A and C (or B and D) is given as \( R_{AC} = 8 \, \Omega \).

3. **Finding the Equivalent Resistance**:
- The resistors AB and CD are in series, and the resistors BC and DA are also in series.
- Therefore, the equivalent resistance for each pair is:
\[ R_{AB} + R_{CD} = R + R = 2R \]
\[ R_{BC} + R_{DA} = R + R = 2R \]

4. **Parallel Combination**:
- Now, the two series combinations (2R and 2R) are in parallel between points A and C:
\[ R_{AC} = \frac{(2R) \times (2R)}{(2R) + (2R)} = \frac{4R^2}{4R} = R \]
- We know that \( R_{AC} = 8 \, \Omega \), so:
\[ R = 8 \, \Omega \]

5. **Finding Resistance Between Adjacent Corners**:
- Now we need to find the resistance between two adjacent corners, say A and B.
- The resistance \( R_{AB} \) is simply the resistance of one resistor:
\[ R_{AB} = R = 8 \, \Omega \]

### Final Answer:
The resistance between any two adjacent corners is \( 8 \, \Omega \).