For the circuit shown in figure, which of the following statements is ture ?

Options

A. Its time constant is `0.25 s`
B. In steady state, current through the inductance will be equal to zero
C. In steady state, current through the battery will be equal to `0.75 A`
D. None of these

Answer

A, C

Explanation

In the circuit shows in the figure in problem, `6 Omega` and `12 Omega` resistances are in parallel with each other and their parallel combination is in series with `4 Omega` and the inductance of `2H`. Hence, equivalent resistance of these three resistance is equal to `8 Omega`.
Therefore, the time constant for the circuit is
`lambda = (L)/(R ) = (2)/(8) = 0.25 s`
Hence (a) is correct.
In steady state, no e.m.f. will be incuced in the inductance. Hence current through the circuit will be equal to `E//R` where `R` is the equivalent resistance. Hence, the steady state current will be equal
to `6//8 = 0.75 A`.
Hence (c ) is correct and (b) is wrong.