Two sources of equal emf are connected to an external resistance R. The internal resistance of the two sources are` R_(1) and R_(2) (R_(1) gt R_(1))`. If the potential difference across the source having internal resistance `R_(2)` is zero, then

Options

A. `R = R_(1)R_(2)//(R_(1) + R_(2))`
B. `R = R_(1)R_(2)//(R_(2) - R_(1))`
C. `R = R_(2) xx (R_(1) +R_(2))//(R_(2) -R_(1))`
D. `R_(2) - R_(1)`

Answer

D

Explanation

`I = (2E)/(R_(1) + R_(2) + R)`
`V_(R_(2)) = 0 rArr E - IR_(2) =0`
`rArr E - (2ER_(2))/(R_(1) + R_(2) + R) = 0 rArr R_(1) +R_(2) + R = 2R_(2)`
`rArr R = R_(2) - R_(1)`