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


We know that the current through the external resistance is the same in both cases, whether the cells are connected in series or parallel. Hence, we can use Ohm's law to find the total emf and total internal resistance for both cases.


When two identical cells are connected in series, the total emf and total internal resistance are given by:
- Total emf = 2E
- Total internal resistance = 2r

where E is the emf of each cell and r is the internal resistance of each cell.

Let's assume the emf and internal resistance of each cell is E and r, respectively. Then, we can write the following equations:
- 2E - 0.5(4) = 0
- 2r + 4 = 4

Solving these equations, we get:
- E = 1.25V
- r = 0.5 ohm

Therefore, the emf and internal resistance of each cell when connected in series are 1.25V and 0.5 ohm, respectively.


When two identical cells are connected in parallel, the total emf and total internal resistance are given by:
- Total emf = E
- Total internal resistance = r/2

where E is the emf of each cell and r is the internal resistance of each cell.

Let's assume the emf and internal resistance of each cell is E and r, respectively. Then, we can write the following equations:
- E - 0.5(4) = 0
- r/2 + 4 = 4

Solving these equations, we get:
- E = 2V
- r = 0.5 ohm

Therefore, the emf and internal resistance of each cell when connected in parallel are 2V and 0.5 ohm, respectively.


- When two identical cells are connected in series, the emf and internal resistance of each cell are 1.25V and 0.5 ohm, respectively.
- When two identical cells are connected in parallel, the emf and internal resistance of each cell are 2V and 0.5 ohm, respectively.

Let voltage of cell be V so. voltage in series = 2V and in parallel = Vlet internal resistance be r so, in series = 2r and in parallel = r/2now, current in series = 2V / 2r+4 (given R= 4 ohm )and current in parallel = V / ( r/2 + 4 )given , current is same so, 2V / 2r + 4 => V /(r/2 +4 ) on solving we get r = 4ohm now according to E = I ( r + R ) put the value of I r and R we get E = 4V