Electric Circuits and Networks

12.6 PROBLEMS

1. The initial currents in L₁ and L₂ in the circuit in Fig. 12.6-1 at t = 0⁻ are 1 A and 0.5 A, respectively, in the directions shown. (i) Write the mesh equations of the circuit. (ii) Obtain the differential equation governing the variation of v_o(t) for t > 0⁺ and calculate the natural frequencies of the circuit. (iii) Obtain the complete response for v_o(t) if v_S(t) = S(t). (iv) Obtain the complete response for v_o(t) if v_S(t) = u(t). (v) Could you have obtained the step response by integrating the impulse response? Explain. (vi) Obtain the total response for the current through L₁ when v_S(t) = u(t) by expressing the total solution as the sum of the natural response terms and the steady-state value and evaluating the amplitude of ...