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

`i= (2E)/(R + r_1 + r_2)`
p.d across `①`
`V_1 = E - ir_1`
`0 = E - (2E)/(R + r_1 + r_2).r_1`
`R + r_1 + r_2 = 2 r_1`
`R = r_1 - r_2`.