Twelve cells, each having emf E volts are connected in series and are kept in a closed box. Some of these cells are wrongly connected with positive and negative terminals reversed. This 12 cell battery is connected in series with an ammeter, an external resistance R ohms and a two-cell battery (two cells of the same type used earlier, connected perfectly in series). The current in the circuit when the 12-cell battery

Step-by-step solution

Let polarity of m cells in a 12 cells battery is reversed, then equivalent emf of the battery =(12-2 m) E Now the circuit can be drawn as : When 12-cell battery and 2-cell battery aid each other, then current through the circuit, i₁= (12-2 m) E+2 E R or 3= (14-2 m) E R ...(i) When they oppose each other, the current through the circuit. i₂= (12-2 m) E-2 E R or 2= (10-2 m) E R ...(ii) Dividing Eq. (i) by (ii), we have 3 2 = 14-2 m 10-2 m or 30-6 m=28-4 m or 2 m=2 m=1