Consider a L-R circuit shown in figure. There is no current in circuit switch S is closed at t = 0, time instant when current in inductor is equal to current in resistor 2R will be :

Options

A. `(L)/(R)l n2`
B. `(2L)/(R) l n2`
C. `(L)/(2R) l n2`
D. `(L)/(2R)`

Answer

A

Explanation

`i_(1)=(V)/(R)(1-e^(-t//tau))rArri_(2)=(V)/(2R)`
`i_(2)=i_(2)rArr(V)/(R)(1-e^(-t//tau))=(V)/(2R)`
`rArr 1-e^(-t//tau)=(1)/(2)rArr e^(-t//tau)=(1)/(2)`
`rArr e^(t//tau)=2 rArr (t)/(tau)=l n2 rArr t = tau l n2=(L)/(R) l n2`.