Switch `S` is closed at time `t=0`. Which one of the following statements is correct?

Options

A. Current in the resistance `R` increases if `E_1r_2 lt E_r(R+r_1)`
B. Current in the resistance `R` increases if `E_1r_2 gt E_2(R+r_1)`
C. Current in the resistance `R` decreases if `E_1r_2 gt E_2(R+r_1)`
D. Current in the resistance `R` decreases if `E_1r_2=E_2 (R+r_1)`

Answer

B

Explanation

Initial current `i_1=(E_1+E_2)/(R+r_1+r_2)`
Final current when second battery is short circuited is
`i_2=E_1/(R+r_1)`
`i_2 lt i_1if E_1/(R+r_1) gt (E_1+E_2)/(R+r_1+r_2)`or
`E_1R+E_1r_1+E_1r_2 gt E_1R+E_1r_1+E_2R+E_2r_1`
or `E_1r_2 gt E_2(R+r_1)`