Refer to the circuit diagram and the corresponding graphs. The current rises when key K is pressed. With R=`R_(1) and L=L_(1)` the rise of current is shown by curve(1), while curve(2) shows the rise of current when `R=R_(2) and L = L_(2)`. The maximum current is same for both curves, then:

Options

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

Answer

D

Explanation

Consider the expression for the current rising exponentially in the LR circuit. The time constant is `(L//R)`. In this case the curve (1) is rising faster than curve (2) indicating that `(L_(1)//R_(1))lt(L_(2)//R_(2))`. However, in both the cases the maximum current is the same and equal to `(V//R_(1)) or (V//R_(2))`. which means `R_(1) = R_(2)`