Two resistances are joined in parallel whose equivolent resistance is `3/5Omega`. One of the resistance wire is broken and the effective resistance becomes `3Omega`. The resistance (in ohms) of the wire that got broken was

Options

A. `4/3`
B. 2
C. `6/5`
D. `3/4`

Explanation

To solve the problem step by step, we will use the concepts of equivalent resistance in parallel circuits.

### Step 1: Understand the given information
We have two resistances \( R_1 \) and \( R_2 \) connected in parallel. The equivalent resistance \( R_{eq} \) of the two resistances is given as \( \frac{3}{5} \, \Omega \). When one of the resistances (let's assume \( R_1 \)) is broken, the effective resistance becomes \( 3 \, \Omega \).

### Step 2: Write the formula for equivalent resistance in parallel
The formula for the equivalent resistance \( R_{eq} \) of two resistances \( R_1 \) and \( R_2 \) in parallel is given by:

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

### Step 3: Substitute the known values into the formula
From the problem, we know:

\[ R_{eq} = \frac{3}{5} \, \Omega \]

Thus, we can write:

\[ \frac{1}{\frac{3}{5}} = \frac{1}{R_1} + \frac{1}{R_2} \]

This simplifies to:

\[ \frac{5}{3} = \frac{1}{R_1} + \frac{1}{R_2} \]

### Step 4: Rearranging the equation
Rearranging gives us:

\[ \frac{1}{R_1} + \frac{1}{R_2} = \frac{5}{3} \]

### Step 5: When one resistance is broken
When \( R_1 \) is broken, the effective resistance becomes \( R_2 \), which is given as \( 3 \, \Omega \). Therefore:

\[ R_2 = 3 \, \Omega \]

### Step 6: Substitute \( R_2 \) into the equation
Now we can substitute \( R_2 \) into our rearranged equation:

\[ \frac{1}{R_1} + \frac{1}{3} = \frac{5}{3} \]

### Step 7: Solve for \( R_1 \)
To isolate \( \frac{1}{R_1} \), we subtract \( \frac{1}{3} \) from both sides:

\[ \frac{1}{R_1} = \frac{5}{3} - \frac{1}{3} = \frac{4}{3} \]

Now, taking the reciprocal gives us:

\[ R_1 = \frac{3}{4} \, \Omega \]

### Step 8: Conclusion
Thus, the resistance of the wire that got broken is:

\[ R_1 = \frac{3}{4} \, \Omega \]