Question

Two sources of current of equal emf are connected in series and having different internal resistance `r_1` and `r_2(r_2gtr_1)`. Find the external resistance `R` at which the potential difference across the terminals of one of the sources becomes equal to zero.

Answer 1

`V=E-ir`
`E` and `i` for both the sources are equal. Therefore, potential difference (`V`) will be zero for a source having greater internal resistance i.e. `r_2`
`:. 0=E-ir_2`
or `E=ir_2=((2E)/(R+r_1_r_2)).r_2`
`:. 2r_2=R+r_1+r_2`
or `R=r_2-r_1`