A cell of emf `epsi` and internal resistance r is connected to two external resistances, `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 0.42 A, 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

The circuit resistance with series combination of `R_1` and `R_2 gt` with resistance `R_1` or `R_2 gt` with parallel combination of `R_1` and `R_2 gt` without any external resistance.
From this we conclude that:
(i) Without any external resistance in the circuit the current should be 4.2 A.
(ii) With resistance `R_1` only the current should be 1.05 A.
(iii) With `R_1` and `R_2` in series combination the current should be 0.42 A.
(iv) With `R_1` and `R_2` in parallel combination the current should be 1.4 A.