Determine the value of t/ at which the current in an LR circuit builds up to 99 % 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 reaches 99 % of its steady-state value, we have I = 0.99 I₀ . Substituting this into the equation: 0.99 I₀ = I₀(1 - e^ -t/ ) 0.99 = 1 - e^ -t/ e^ -t/ = 0.01 Taking the natural logarithm on both sides: - t = (0.01) - t = (10⁻²) - t = -2 (10) Using the value (10) 2.303 : t = 2 2.303 = 4.606 4.6