A cell of emf `epsilon` and internal resistance r gives a current of 0.5 A with an external resistance of `12 Omega` and a current of 0.25 A with an external resistance of `25 Omega`. Calculate (a) internal resistance of the cell and (b) emf of the cell.

Explanation

To solve the problem, we will use Ohm's law and the concept of internal resistance in a circuit. We have two scenarios with different external resistances and currents, which will help us derive two equations to find the internal resistance (r) and the emf (ε) of the cell.

### Step-by-Step Solution:

1. **Write the equations based on Ohm's law:**
For a cell with emf ε and internal resistance r, the current I through an external resistance R is given by:
\[
I = \frac{\epsilon}{R + r}
...