A cell of emf E and internal resistance r is connected to two external resistance `R_(1) " and " R_(2)` and a perfect ammeter. The current in the circuit is measured in four different situations :
(i) without any external resistance in the circuit
(ii) with resistance `R_(1)` only
(iii) with `R_(1) " and " R_(2)` in series combination
(iv) with `R_(1) " and " R_(2)` in parallel combination
The currents measured in the four cases are 0.42A, 1.05 A, 1.4 A and 4.2 A, but not necessarily in that order. Identify the currents corresponding to the four cases mentioned above.

Explanation

To solve the problem, we need to analyze the four situations in which the current is measured and identify which current corresponds to each situation.

### Step-by-Step Solution:

1. **Situation (i): Without any external resistance**
- In this case, the only resistance in the circuit is the internal resistance \( r \) of the cell. The current will be maximum because there are no external resistances to limit it.
- The maximum current can be calculated using Ohm's law:
\[
...