An LR circuit has a time constant of 40 ms . The circuit is connected at t = 0 and the steady-state current is found to be 2.0 A . Determine the current at t = 10 ms .

Step-by-step solution

The growth of current in an LR circuit is given by the equation: I(t) = I₀ (1 - e^ -t/ ) Given I₀ = 2.0 A , = 40 ms , and t = 10 ms . Substituting the values into the equation: I(10 ms ) = 2.0 (1 - e^ -10/40 ) I(10 ms ) = 2.0 (1 - e^ -0.25 ) Using the approximate value e^ -0.25 0.7788 : I(10 ms ) = 2.0 (1 - 0.7788) I(10 ms ) = 2.0 0.2212 = 0.4424 A Rounding to two decimal places, the current is 0.44 A .