Question 66: Current Electricity

Question

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

Accepted Answer

When cells are connected in series, the total electromotive force (emf) of the battery is the sum of the individual cell voltages. This assumes all cells are oriented correctly, with positive to negative in a chain. If a cell is connected in the opposite direction, its voltage subtracts from the total rather than adds to it.
In this problem, we have a total of 12 cells, each with an emf of $$5\,V$$. Normally, if all were connected correctly in series, the total emf would be:
$$
	ext{Total emf} = 	ext{Number of cells} 	imes 	ext{emf of each cell}
$$

$$
	ext{Total emf} = 12 	imes 5\,V = 60\,V
$$
However, 3 cells are connected incorrectly, which means their voltage contribution would be negative instead of positive. So, for these 3 cells, instead of adding $$3 	imes 5\,V$$, we subtract $$3 	imes 5\,V$$:
$$
	ext{Adjusted total emf} = 	ext{Total emf without errors} - 2 	imes (	ext{emf of 3 wrong cells})
$$

$$
	ext{Adjusted total emf} = 60\,V - 2 	imes 15\,V
$$

$$
	ext{Adjusted total emf} = 60\,V - 30\,V = 30\,V
$$
Therefore, the resultant emf of the battery, taking into account the 3 incorrectly connected cells, is 30 V. This corresponds to Option B.

Answer

90V

Answer

30V

Answer

60V

Answer

45V

Current Electricity

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

Choose the correct answer: