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

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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.

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.

 

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