An LR circuit with L = 1.0 H and R = 20 is connected across a 2.0 V emf at t = 0 . Determine the rate of change of current di/dt at t = 100 ms .

Step-by-step solution

The equation for the growth of current in an LR circuit is given by i = i₀ (1 - e^ -t/ ) where i₀ = V R is the steady state current and = L R is the time constant. The rate of change of current is di dt = d dt [ V R (1 - e^ -Rt/L ) ] = V L e^ -Rt/L Given values are V = 2.0 V , L = 1.0 H , R = 20 , and t = 100 ms = 0.1 s . Substituting these values, we get di dt = 2.0 1.0 e^ -20 0.1 / 1.0 di dt = 2.0 e⁻² Using e 2.718 , we have e^2 7.389 . di dt = 2.0 7.389 0.27 A s ⁻¹