Four wires of equal length and of resistance 5ohm each are connected in the form of a square. The equivalent resistance between the diagonally opposite corners of the square is

Options

A. 5 ohm
B. 10 ohm
C. 20 ohm
D. 5/4 ohm

Answer

To find the equivalent resistance between the diagonally opposite corners of a square formed by four resistors of equal resistance (5 ohms each), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Configuration**:
- We have four resistors, each with a resistance of 5 ohms, arranged in the shape of a square. Let's label the corners of the square as A, B, C, and D. The resistors are connected as follows:
- Resistor 1 (R1) between A and B
- Resistor 2 (R2) between B and C
- Resistor 3 (R3) between C and D
- Resistor 4 (R4) between D and A

2. **Identify the Points of Interest**:
- We need to find the equivalent resistance between points A and C (the diagonally opposite corners).

3. **Analyze the Circuit**:
- The resistors R1 and R3 (between A-B and D-C) are in series with each other, and the resistors R2 and R4 (between B-C and A-D) are also in series with each other.
- Therefore, we can consider the two paths from A to C:
- Path 1: A to B (R1) and B to C (R2)
- Path 2: A to D (R4) and D to C (R3)

4. **Calculate the Resistance for Each Path**:
- For Path 1 (A to B to C):
\[ R_{AB-C} = R1 + R2 = 5 \, \Omega + 5 \, \Omega = 10 \, \Omega \]
- For Path 2 (A to D to C):
\[ R_{AD-C} = R4 + R3 = 5 \, \Omega + 5 \, \Omega = 10 \, \Omega \]

5. **Combine the Two Paths**:
- The two paths (A-B-C and A-D-C) are in parallel. The equivalent resistance \( R_{eq} \) for two resistors in parallel can be calculated using the formula:
\[ \frac{1}{R_{eq}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \]
- Substituting the values:
\[ \frac{1}{R_{eq}} = \frac{1}{10 \, \Omega} + \frac{1}{10 \, \Omega} = \frac{2}{10} = \frac{1}{5} \]
- Therefore, the equivalent resistance is:
\[ R_{eq} = 5 \, \Omega \]

### Final Answer:
The equivalent resistance between the diagonally opposite corners of the square is **5 ohms**.