In a potentionmeter experiment, when three cells A, B and C are connected in series, the balancing length is found to be 740 cm. If A and B are connected in series, balancing length is 440 cm and for B and C connected in series, it is 540 cm. The emf of `E_(A),E_(B)` and `E_(C)` are respectively (in volts)

Options

A. 1,1.2 and 1.5
B. 1,2 and 3
C. 1.5, 2 and 3
D. 1.5, 2.5 and 3.5

Answer

A

Explanation

`E_(A) + E_(B) + E_( C) = kl_(1) = k xx 740`
`E_(A) + E_(B) = kl_(2) = k xx 440`
`E_(B) + E_( C) = kl_(3) = k xx 540`
`E_( C) = 740k - 440 k = 300 k`
`E_(B) = 240 k`
`E_(A) = 200 k`
`E_(A) : E_(B): E_( C) = 200 k:240k:300k`
`=10:12:15=1:12:1.5`
`E_(A) = 1V, E_(B) = 1.2 V, E_( C) = 1.5 V`