Final answer:
To find the time when the power at the terminals of the inductor is zero, we need to determine the current and voltage expressions at different time ranges, calculate the power at those times, and solve for t when the power is zero.
Step-by-step explanation:
To find the time when the power at the terminals of the inductor is zero, we need to determine the current and voltage expressions at different time ranges and then calculate the power at those times. Given that the voltage across the inductor is 60 V at t=0 and the current expression is i(t) = A1e^-2000t + A2e^-8000t, we can substitute these values into the power equation P = VL(t) * i(t), where VL(t) is the voltage across the inductor.
By substituting the given values, we obtain the expression P(t) = (60e^-t/15) * (A1e^-2000t + A2e^-8000t). To find the time(s) when the power is zero, we set P(t) equal to zero and solve for t. However, before that, we need to determine the values of A1 and A2 by applying the initial condition when t=0, where i(t)=1A.
Using the initial condition, we get 1A = A1 + A2. We can also solve for A1 and A2 individually by taking the derivative of i(t) with respect to t and substituting t=0 in the derivative expression. By equating the calculated values of A1 and A2, we can solve for them and then substitute them into the power expression. Finally, by setting the power expression equal to zero, we can solve for t and obtain the time(s) when the power at the terminals of the inductor is zero.