Question

two identical cells whether joined in series or in parallel gives the same current when connected to an external resistance of 1ohm. find the internal resistance of each cell.

Answer 1

let the resistance of the two cells be 'r'

now,

when joined in series

R_S = r + r + 1

or

R_S = 2r + 1

the series current in this case would be

I_S= V/R = 2E/R_S

[V = E + E - total emf]

or

I_S = 2E / (2r + 1)

and

when joined in parallel

1/R_P = (1/r) + (1/r) + 1

or

R_P = 1 + r/2

the parallel current in this case would be

I_P = V/R_P = E/R_P

or

I_P = E / (1 + r/2)

now,

we are given

I_S = I_P

so,

2E / (2r + 1) = E / (1 + r/2)

or

2 + r = 2r + 1

thus,

r = 1 ohm