EAMCET Engineering 2006 Solved Paper

Let polarity of m cells in a 12 cells battery is reversed, then equivalent emf of the battery
=(12−2m)E
Now the circuit can be drawn as :
When 12-cell battery and 2-cell battery aid each other, then current through the circuit,
i1=‌

(12−2m)E+2E

R

or ‌‌3=‌

(14−2m)E

R

. . . (i)
When they oppose each other, the current through the circuit.
i2=‌

(12−2m)E−2E

R

or ‌‌2=‌

(10−2m)E

R

. . . (ii)
Dividing Eq. (i) by (ii), we have
‌

3

2

=‌

14−2m

10−2m

or 30−6m=28−4m
or ‌‌2m=2
∴‌‌m=1