Two cells, having the same emf, are connected in series through an external resistance `R`. Cells have internal resistance `r_(1)` and `r_(2) (r_(1) gt r_(2))` respectively. When the circuit is closed, the potentail difference across the first cell is zero the value of `R` is

Options

A. `r_(1) + r_(2)
B. `r_(1) - r_(2)
C. `(r_(1) + r_(2))/(2)`
D. `(r_(1) - r_(2))/(2)`

Answer

B

Explanation

(b) Let the voltage across any one cell is `V`, then
`V = E - ir = E - r_(1) ((2E)/(r_(1) + r_(2) + R))`
But `V = 0`
`implies E - (2Er_(1))/(r_(1) + r_(2) + R) = 0`
`r_(1) + r_(2) + R = 2 r_(1)`
`implies R = r_(1) - r_(2)`