A cell of unknown EMF E and internal resistance r, two unknown resistances R₁ and R₂ (R₂>R₁) and a perfect ammeter are given. The current in the circuit is measured in five different situations : 

1. without any external resistance in the circuit,
2. with resistance R₁ only,
3. with resistance R₂ only,
4. with both R₁ and R₂ used in series combination, and 
5. with both R₁ and R₂ used in parallel combination.

The current obtained in the five cases are 0.42 A, 0.6 A, 1.05 A, 1.4 A and 4.2 A, but not necessarily in that order.

In terms of r, what is the value of EMF of the cell ?

4.2 r

$ \frac{E}{r} = 4.2$ .........(1)

$\frac{E}{r+R_1} = 1.05 A$ .......(2)

$\frac{E}{r+R_2} = 0.6 A$ ...........(3)

$\frac{E}{r+R_1+R_2} = 0.42A$ ........(4)

$\frac{E}{r + \frac{R_1 R_2}{R_1+R_2}} = 1.4A$ ...........(5)

From Equation (1) ,$ E = 4.2r$