Problem 예제.

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다음과 같은 2개의 전류의 초기값 $i_1(0_+), \quad i_2(0_+)$ 가 옳게 구해진 것은?

$I_1(s) = \dfrac{12(s+8)}{4s(s+6)}, \quad I_2(s) = \dfrac{12}{s(s+6)}$

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4, 2

3, 0

3, 4

4, 0

Solution

$\lim_{t \to 0} i(t) = \lim_{s \to \infty} s I(s)$

$\lim_{t \to 0} i(t) = \lim_{s \to \infty} s \dfrac{12(s+8)}{4s(s+6)} = \lim_{s \to \infty} \dfrac{12s^2(1+8/s)}{4s^2(1+6/s)} = 3$

$\lim_{t \to 0} i(t) = \lim_{s \to \infty} s \dfrac{12}{s(s+6)} = \lim_{s \to \infty} \dfrac{12}{s+6} = \dfrac{12}{\infty} = 0$

Correct answer: 2