Question

Two identical cells whether joined together in series
or in parallel give the same current, when connected
to external resistance of 2ohm . Their internal
resistance ris
(1) 2ohm
(2) 1ohm
(3) 1.5ohm
(4) 4ohm​

Answer 1

We have the two equations:

For series combination,

I=nE/ R+nr                  n---is  two since there are two identical cells.

0.5=2E/ 4+2r ⇒ 2+r=2E ⇒ 2E-r=2   _(1)

For parallel combination,

I=mE/ mR+r                m----is used as a different variable but its value is 0.5= 2E/ 2*4 +r

4+0.5r=2E

2E-0.5r=4      _(2)

Multiply (2) with 2

4E-r = 4     _(3)

Subtracting 3 from 1 :

4E-r=4

2E-r=2

2E=2

E=1 V

Applying the value of E in (1)

2*1-r=2

r=2+2=4 ohms