A battery of unknown emf and internal resistance is given to a student for the experiment. When student connects the battery to an external resistance of `10 Omega` then 1A current flows through the circuit and when the same is connected to `15 Omega` resistance then 0.75 A current flows through the circuit . Calculate the emf and internal resistance of the given battery.

Explanation

To solve the problem, we need to use the information provided about the current flowing through the circuit with different external resistances. We can derive two equations based on Ohm's law and the concept of internal resistance.

### Step-by-Step Solution:

1. **Understanding the Circuit**:
- When the battery is connected to an external resistance \( R_1 = 10 \, \Omega \), the current \( I_1 = 1 \, A \) flows through the circuit.
- When the battery is connected to an external resistance \( R_2 = 15 \, \Omega \), the current \( I_2 = 0.75 \, A \) flows through the circuit.

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