When the switch is open in lowerpoint loop of a potentiometer, the balance point length is `60 cm`. When the switch is closed with a known resistance of `R=4Omega` the balance point length decreases to `40 cm`. Find the internal resistance of the unknown battery.

Explanation

To solve the problem, we will use the principles of a potentiometer and Ohm's law. Here’s a step-by-step solution:

### Step 1: Understand the Setup
When the switch is open, the balance point is at 60 cm. This means the potential difference across this length is equal to the EMF (E) of the unknown battery. When the switch is closed, the balance point changes to 40 cm.

### Step 2: Write the Equations for Each Case
1. **When the switch is open:**
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