The switch is closed at $t=0$, find values of $i(t), \frac{d i(t)}{d t}, \frac{d^2 i(t)}{d t^2}$ at $t=0$ Assume all initial conditions are zero.

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The switch is closed at

$t=0$ , find values of

$i(t), \frac{d i(t)}{d t}, \frac{d^2 i(t)}{d t^2}$ at

$t=0$ Assume all initial conditions are zero.

written 2.5 years ago by

prajapatijaimin • 3.3k

• modified 2.5 years ago

The switch is closed at $t=0$ , find values of $i(t):

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electrical network analysis and system

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1 Answer

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written 2.5 years ago by

prajapatijaimin • 3.3k

Solution:

$\because$ All initial conditions are zero $\therefore I_L(\overline{0})=I_0=0$ Amp ckt at $t=0^{+}$

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Apply KVL to loop

$\begin{gathered} \\ 100-10 i(t)-1 \cdot \frac{d i(t)}{d t}=0...(1) \\\\ \text { put } t=0^{+}: \frac{d i\left(0^{+}\right)}{d t}=0 \\\\ 100-10 i\left(0^{+}\right)-\frac{d i\left(0^{+}\right)}{d t}=100 \quad \text { A/s } \\ \end{gathered} \\$

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Differentiating $e q-n$ (1)

$0-10 \frac{d i(t)}{d t}-\frac{d^2 i(t)}{d t^2}=0 \\$

$put$

$t=0^{+} \\\$

$-10 \frac{d i\left(0^{+}\right)}{d t}-\frac{d^2 i\left(0^{+}\right)}{d t^2}=0 \\$

$-10(100)=\frac{d^2 c\left(0^{+}\right)}{d t^2} \\$

$\frac{d^2 i\left(0^{+}\right)}{d t^2}=-1000 \mathrm{~A} / \mathrm{s}^2 \\$

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