Two cells each emf e but of internal resistance `r_1` and `r_2` are connected in series through and external resistance R. IF the potential difference across the first cell is zero while current flows the value of R in terms of `r_1` and `r_2` is

Options

A. `R=r_1+r_2`
B. `R=r_1-r_2`
C. `R=1/2(r_1+r_2)`
D. `R=1/2(r_1-r_2)`

Answer

B

Explanation

Main current , I=`(t otal emf)/(t otal resistance)`
`thereforeI=(2e)/(r_1+r_2+R)`
Again, potential difference =E-1
As the potential across the first cell is zero, when current flows through it
`therefore 0=e-(2e)/(r_1+r_2+R)timesr_1thereforeR=r_1-r_2`