The correct option is
B 1Let n be the number of wrongly connected cells.
number of cells helping one another =(12−n)
Total e.m.f. of such cells =(12−n)E
Total e.m.f. of cells opposing =nE
Resultant e.m.f of battery =(12−n)E−nE=(12−2n)E
Total resistance of cells =12r
( ∵ resistance remains same irrespective of connection of cells )
With additional cells
(a) Total e.m.f. of cells when additional cells help battery =(12−2n)E+2E
Total resistance =12r+2r=14r
∴(12−2n)E+2E14r=3 .......(i)
(b) similarly when additional cells oppose the battery
(12−2n)E−2E14r=2 ....(ii)
Solving (i) and (ii), n=1