Current growth in two L-R circuits (b) and (c ) as shown in figure (a). Let `L_(1), L_(2), R_(1)` and `R_(1)` be the corresponding values in two circuits. Then

Options

A. `R_(1)gtR_(2)`
B. `R_(1)=R_(2)`
C. `L_(1)gtL_(2)`
D. `L_(1)ltL_(2)`

Answer

B, D

Explanation

Since maximum current passing through two circuits is same and equal to `V//R_(1)` in (b) and `V//R_(2)` in (c) then `R_(1)=R_(2)`
Current growth equation of `L-R` circuit is:
`i=i_(0)(1-e^(-t//tau))`
`i=I_(0)(1-e^((-tR)/L))`
Now, `(di)/(dt)=(i_(0)R)/L e^(-tR//L)`
At `t=0` slope of I vs `t` curve:
`(di)/(dt)=(i_(0)R)/L`
From graph (a): slope of curve (b) `gt` slope of curve (c) ltbgt `(R_(1))/(L_(1)) gt (R_(2))/(L_(2))`
Since `R_(1)=R_(2)`
`L_(1)ltL_(2)`