A battery of emf `epsilon` and internal resistance r sends currents `I_(1)` and `I_(2)`, when connected to external resistance `R_(1)` and `R_(2)` respectively. Find the emf and internal resistance of the battery.

Explanation

To find the emf (ε) and internal resistance (r) of the battery given the currents I₁ and I₂ when connected to external resistances R₁ and R₂ respectively, we can follow these steps:

### Step 1: Write the equations for the two scenarios
When the battery is connected to the external resistance R₁, the current flowing through it is I₁. According to Ohm's law, the voltage across the external resistance and the internal resistance can be expressed as:
\[ \epsilon = I_1 R_1 + I_1 r \]
(1)
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