Determine the value of t/ at which the current in an LR circuit builds up to 99.9 % 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/ ) Given that the current builds up to 99.9 % of its steady-state value, we have I = 0.999 I₀ . Substituting this into the equation: 0.999 I₀ = I₀ (1 - e^ -t/ ) 0.999 = 1 - e^ -t/ e^ -t/ = 1 - 0.999 = 0.001 e^ -t/ = 10⁻³ Taking the natural logarithm on both sides: - t = (10⁻³) - t = -3 (10) Using the value (10) 2.303 : t = 3 2.303 = 6.909 6.9