Question

A battery is made of 12 cells having emf 5 V each. If three cells are unknowingly connected wrong, the resultant emf of the battery will be:

• A. 90 V
• B. 30 V
• C. 60 V
• D. 45 V

Hint:

In a battery made of cells, when cells are connected in the wrong direction, their emf contributes negatively to the total emf. The total emf is the sum of the emfs of the correctly connected cells minus the emfs of the incorrectly connected cells.

Answer 1

The Correct Option is B

We are given a battery made of 12 cells, each with an emf of 5 V. Normally, when all the cells are connected correctly, the total emf of the battery would be the sum of the emfs of all the cells. In this case, the total emf with all cells connected in the same direction would be: \[ \text{Total emf} = 12 \times 5 \, \text{V} = 60 \, \text{V} \] Now, three cells are connected wrong, which means they are connected in the opposite direction. This will reduce the total emf, as the emfs of these cells will subtract from the total emf instead of adding to it. Each wrongly connected cell has an emf of 5 V, so the emf contributed by the three wrongly connected cells is: \[ \text{Emf of wrongly connected cells} = 3 \times 5 \, \text{V} = 15 \, \text{V} \] Since the wrong connection subtracts from the total emf, the resultant emf of the battery is: \[ \text{Resultant emf} = 60 \, \text{V} - 2 \times 15 \, \text{V} = 30 \, \text{V} \] Thus, the resultant emf of the battery will be 30 V. Therefore, the correct answer is Option (B): 30 V.