Two cells, one of EMF 12 V and internal resistance 1 and another of unknown EMF E ( E < 12 V ) and internal resistance 2 , are connected in series such that their positive terminals are joined together. This combination is connected across an external circuit consisting of a 3 resistor in series with a parallel combination of a 4 and a 12 resistor. If the current flowing through the 4 resistor is 0.75 A , the value o

Step-by-step solution

The equivalent resistance of the parallel combination of 4 and 12 resistors is: R_p = 4 12 4 + 12 = 48 16 = 3 The total external resistance of the circuit is: R_ ext = 3 + 3 = 6 The total resistance of the entire circuit, including the internal resistances of the cells, is: R_ total = R_ ext + r₁ + r₂ = 6 + 1 + 2 = 9 Let the total current in the main circuit be I . Using the current divider rule, the current through the 4 resistor is: I₄ = I 12 4 + 12 = I 12 16 = I 3 4 Given that I₄ = 0.75 A , we have: 0.75 = I 0.7