A circuit using a potentiometer and battery of negligible internal resistance is set up as shown in Fig. to develop a constant potential gradient along the wire AB. Two cells of emfs `epsi_1` and `epsi_2` are connected in series as shown in combinations (1) and (2). The balance points are obtained respectively at 400 cm and 240 cm from the point A. Find (i) `epsi_1/epsi_2` , (ii) balancing length for the cell `epsi_1` only .

Explanation

If k be the potential gradient along the potentiometer wire, then as per data given we have :
`epsi_1 + epsi_2 = k xx 400 cm ` ...(i) and `epsi_2 - epsi_1 = k xx 250 cm` ...(ii)
`rArr epsi_1 = 75k` and `epsi_2 = 325 k`
` therefore epsi_1/epsi_2 = (75k)/(325k) = 3/13`
If balancing length for the cell `epsi_1` only be l cm, then `epsi_1 = lk `. but `epsi_1 = 75k rArr l = 75 cm `