Question

12 cells, each having the same emf are connected in series and are kept in a closed box. Some of the cells are wrongly connected. The battery is in series with an ammeter and two cells of identical nature to others. The current is 3A when external cells aid the battery and 2A when they oppose. How many cells are wrongly connected in the battery?

Answer 1

A reverse cell decreases the emf by 2 ε. Let ‘n’ cells be in opposition, then in the first connection 12ε – 2nε + 2ε = 3R
14ε – 2 nε = 3R … (1) where R is the effective resistance of the closed circuit. Similarly in opposition with external cells, 12 ε – 2nε – 2ε = 2R
i.e., 10ε – 2nε = 2R … (2)
28 – 4n = 30 – 6n
∴ 2n = 2           ∴ n = 1