Determine the value of t/ at which the current in an LR circuit builds up to 90 % of the steady-state value.

Step-by-step solution

The growth of current in an LR circuit is given by the equation: I = I₀(1 - e^ -t/ ) where I₀ is the steady-state current and is the time constant. Given that the current builds up to 90 % of its steady-state value, we have I = 0.9 I₀ . Substituting this into the equation gives: 0.9 I₀ = I₀(1 - e^ -t/ ) 0.9 = 1 - e^ -t/ e^ -t/ = 0.1 Taking the natural logarithm on both sides: - t = (0.1) t = (10) t 2.3