At t = 0 , an LR circuit with L = 1.0 ext H and R = 20 ext is connected across an emf of 2.0 ext V . What is the value of the self-induced emf in the circuit at t = 100 ext ms ?

Step-by-step solution

The time constant of the LR circuit is given by: = L R = 1.0 20 = 0.05 s The current in the circuit at any time t is: I = E R (1 - e^ -t/ ) The magnitude of the self-induced emf is: |e| = L dI dt = L d dt [ E R (1 - e^ -t/ ) ] |e| = L E R ( 1 e^ -t/ ) Substituting = L R gives: |e| = E e^ -t/ Substituting the given values E = 2.0 V and t = 100 ms = 0.1 s : |e| = 2.0 e^ -0.1 / 0.05 = 2.0 e⁻² Using the value e⁻² 0.1353 : |e| = 2.0 0.1353 = 0.2706 V 0.27 V