When a resistance of 12 ohm is connected across a cell, its terminal potential difference is balanced by 120 cm length of potentiometer wire. When the resistance of 18 ohm is connected across the same cell, the balancing length is 150 cm. Find the balancing length when the cell is in open circuit. Also calculate the internal resistance of the cell.

Explanation

To solve the problem, we need to find the balancing length when the cell is in open circuit and also calculate the internal resistance of the cell using the given data.

### Given:
1. When a resistance of \( R_1 = 12 \, \Omega \) is connected, the balancing length \( L_1 = 120 \, \text{cm} \).
2. When a resistance of \( R_2 = 18 \, \Omega \) is connected, the balancing length \( L_2 = 150 \, \text{cm} \).

### Step 1: Set up the equations
The potential difference across the cell when a resistance is connected can be expressed in terms of the balancing lengths and resistances as follows:
...