Solution Found!
The voltage v(t) and current i(t) of a 0.5-H inductor adhere to the passive convention
Chapter 7, Problem P7.5-7(choose chapter or problem)
The voltage v(t) and current i(t) of a 0.5-H inductor adhere to the passive convention. Also, v(0) = 0 V, and i(0) = 0 A.
(a) Determine v(t) when i(t) = x(t), where x(t) is shown in Figure P 7.5-7 and i(t) has units of A.
(b) Determine i(t) when v(t) = x(t), where x(t) is shown in Figure P 7.5-7 and v(t) has units of V.
Hint: x(t) = 0.2t - 0.4 when 2 < t < 6.
Questions & Answers
QUESTION:
The voltage v(t) and current i(t) of a 0.5-H inductor adhere to the passive convention. Also, v(0) = 0 V, and i(0) = 0 A.
(a) Determine v(t) when i(t) = x(t), where x(t) is shown in Figure P 7.5-7 and i(t) has units of A.
(b) Determine i(t) when v(t) = x(t), where x(t) is shown in Figure P 7.5-7 and v(t) has units of V.
Hint: x(t) = 0.2t - 0.4 when 2 < t < 6.
ANSWER:
Step 1 of 3
Finding when :
Recall the relation across an inductor. Since we know , we can find by deriving. However, since is a piecewise function, we must split our expression for where the function changes.