At t = 0 , an LR circuit having L = 1.0 H and R = 20 is connected across an emf of 2.0 V . Find the rate of change of current di/dt at t = 200 ms .

Step-by-step solution

The current in an LR circuit at time t is given by i = E R (1 - e^ -Rt/L ) Differentiating with respect to t , the rate of change of current is: di dt = E L e^ -Rt/L Given E = 2.0 V , L = 1.0 H , R = 20 , and t = 200 ms = 0.2 s Substituting the values: di dt = 2.0 1.0 e^ -20 0.2 / 1.0 di dt = 2 e⁻⁴ Using e⁻⁴ 0.0183 : di dt = 2 0.0183 = 0.0366 A s ⁻¹ 0.037 A s ⁻¹