In potentiometer experiment when terminates of the cell is at distance of 52 cm, then no current flows through it. When `5ohm` shunt resistance is connected in it then balance length is at 40 cm. The internal resistance of the cell is

Options

A. 5
B. `200/52`
C. `52/8`
D. 1.5

Explanation

To find the internal resistance of the cell in the potentiometer experiment, we can follow these steps:

### Step 1: Understand the given information
- The balance length without shunt resistance (L1) = 52 cm
- The balance length with shunt resistance (L2) = 40 cm
- The shunt resistance (R) = 5 ohms

### Step 2: Calculate the difference in balance lengths
The difference in balance lengths is given by:
\[ L1 - L2 = 52 \, \text{cm} - 40 \, \text{cm} = 12 \, \text{cm} \]

### Step 3: Use the potentiometer formula
The formula for internal resistance (r) of the cell in terms of the lengths and the shunt resistance is:
\[ r = R \cdot \frac{L1 - L2}{L2} \]

### Step 4: Substitute the known values into the formula
We already calculated \( L1 - L2 = 12 \, \text{cm} \) and we know:
- \( L2 = 40 \, \text{cm} \)
- \( R = 5 \, \text{ohms} \)

Substituting these values into the formula:
\[ r = 5 \cdot \frac{12}{40} \]

### Step 5: Simplify the expression
Calculating the fraction:
\[ \frac{12}{40} = \frac{3}{10} = 0.3 \]

Now substituting back:
\[ r = 5 \cdot 0.3 = 1.5 \, \text{ohms} \]

### Final Answer
The internal resistance of the cell is \( 1.5 \, \text{ohms} \).

---