When two resistance are connected in parallel then the equivalent resistance is `(6)/(5)Omega` When one of the resistance is removed then the effective resistance is `2Omega`. The resistance of the wire removed will be

Options

A. 3 ohm
B. 2 ohm
C. `(3)/(5)ohm`
D. `(6)/(5)ohm`

Explanation

To solve the problem, we need to find the resistance of the wire that was removed when two resistances are connected in parallel. We are given the following information:

1. The equivalent resistance of the two resistances in parallel is \( \frac{6}{5} \, \Omega \).
2. When one of the resistances is removed, the effective resistance becomes \( 2 \, \Omega \).

Let's denote the two resistances as \( R_1 \) and \( R_2 \).

### Step 1: Write the formula for equivalent resistance in parallel
The formula for the equivalent resistance \( R_{eq} \) of two resistances \( R_1 \) and \( R_2 \) connected in parallel is given by:

\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} \]

### Step 2: Substitute the known equivalent resistance
We know that the equivalent resistance is \( \frac{6}{5} \, \Omega \). Therefore, we can write:

\[ \frac{1}{\frac{6}{5}} = \frac{1}{R_1} + \frac{1}{R_2} \]

This simplifies to:

\[ \frac{5}{6} = \frac{1}{R_1} + \frac{1}{R_2} \]

### Step 3: Write the equation when one resistance is removed
When one of the resistances (let's say \( R_2 \)) is removed, the effective resistance becomes \( R_1 = 2 \, \Omega \).

### Step 4: Substitute \( R_1 \) into the equivalent resistance equation
Now we substitute \( R_1 = 2 \, \Omega \) into the equation we derived in Step 2:

\[ \frac{5}{6} = \frac{1}{2} + \frac{1}{R_2} \]

### Step 5: Solve for \( R_2 \)
To solve for \( R_2 \), we first convert \( \frac{1}{2} \) to a common denominator:

\[ \frac{5}{6} = \frac{3}{6} + \frac{1}{R_2} \]

Now, rearranging gives:

\[ \frac{1}{R_2} = \frac{5}{6} - \frac{3}{6} = \frac{2}{6} = \frac{1}{3} \]

Taking the reciprocal:

\[ R_2 = 3 \, \Omega \]

### Conclusion
The resistance of the wire that was removed is \( R_2 = 3 \, \Omega \).