Two identical cells either in series or parallel in combination give the same current of 0.5A through an external resistance of 4ohm. Find the emf and internal resistance of each cell.




When two identical cells are connected in series or parallel, the total current passing through the external resistance is the same. Hence, the total current is given by:

I = 0.5A


When two identical cells are connected in series or parallel, the equivalent resistance is given by:

For series combination: Req = 2r

For parallel combination: Req = r/2

Where r is the internal resistance of each cell.

Since the current is same in both cases, the equivalent resistance must be the same. Therefore, we have:

2r = 4ohm or r/2 = 4ohm


Solving the above equations, we get:

r = 2ohm


The EMF of each cell can be found using the formula:

E = V + Ir

Where E is the EMF of the cell, V is the terminal voltage, I is the current passing through the cell, and r is the internal resistance of the cell.

For series combination, the current passing through each cell is half of the total current. Hence, we have:

E = V + (0.5A/2) x 2ohm

E = V + 0.5V

E = 1.5V

For parallel combination, the current passing through each cell is the same as the total current. Hence, we have:

E = V + 0.5A x 2ohm

E = V + 1V

E = 2V

Therefore, the EMF of each cell is:

For series combination: 1.5V

For parallel combination: 2V


The internal resistance of each cell is 2ohm and the EMF of each cell is 1.5V for series combination and 2V for parallel combination.