Question

Two identical cells whether they are joined in series or parallel, give the same current when connected to a load resistance of 1 ohm. Find the internal resisitanceof 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