Consider a simple circuit shown in Fig. 2(ET).2. stands for a variable resistance R'.R' can vary from `R_(0)` to infinity. r is internal resistance of the battery `(rltltRltltlR_(0))`

Options

A. Potential drop across AB is nearly constant as R' is varied
B. Current through R' is nearly a constant as R' is varied
C. Current I depends sensitively on R'
D. `Ige(V)/(r+R)` always

Answer

A, D

Explanation

Current, `I=(V)/(r+(R R')/(R+R')) "As" R'gtgtR, "so" R+R'geR'` Hence, `I=(V)/(r+RR'//R')ge(V)/(r+R)`
Thus, option (d) is correct. Potential difference across A and B, `v_(AB)=Ixx(R R')/(R+R')`
`thereforev_(AB)=(V)/(r+(R R'//R+R'))xx(R R')/((R+R'))=(VxxR R')/(r(R+R')+R R')=(VxxR R')/(r R'+R R')=(VR)/(r+R) [becauseR+R'=R']`
`therefore V_(AB)` is constant if R' is varied Hence, option (a) is correct.
Current through `R', I'=(V_(AB))/(R)'=(VR)/((r+R)R')=(VR)/(r R'+R R')`
Thus l' is not constant as R' is varied. The current I does not depend on the senstivity of R'