The emf of a cell is `epsilon` and its internal resistance is r. its terminals are connected to a resistance R. The potential difference between the terminals is `1.6V` for `R = 4 Omega`, and `1.8 V` for `R = 9 Omega`. Then,

Options

A. `epsilon = 1 V, r = 1 Omega`
B. `epsilon = 2 V, r = 1 Omega`
C. `epsilon = 2 V, r = 2 Omega`
D. `epsilon = 2.5 V, r = 0.5 Omega`

Answer

B

Explanation

`V_A - V_B = E - ir = {E - ( E)/(r + R) .r } = (ER)/(R + r)`
`1.6 = (E(4))/(4 + r)` …(i)
`1.8 = (E(9))/(9 + r)` …(ii)
(i)//(ii) `rArr (1.6)/(1.8) = (4)/(9).((9 + r))/((4 + r))`
`(8)/(9) =(4)/(9).((9 + r))/((4 + r))`
`8 + 2r = 9 + r`
`r = 1 Omega`
`E = 2 V`.