Power in the circuit is expressed as:

$\overline{){\mathbf{P}}{\mathbf{=}}{\mathbf{V}}{\mathbf{i}}}$, where **V** is voltage and **i** is current.

Total energy delivered to the element is found from:

$\overline{){\mathbf{w}}{\mathbf{=}}{{\mathbf{\int}}}_{{\mathbf{0}}}^{{\mathbf{\infty}}}{\mathbf{p}}{\mathbf{\left(}}{\mathbf{t}}{\mathbf{\right)}}{\mathbf{d}}{\mathbf{t}}}$

**a)**

From the equation for power:

$\begin{array}{rcl}\mathbf{P}& \mathbf{=}& \mathbf{V}\mathbf{i}\\ & \mathbf{=}& \mathbf{(}\mathbf{75}\mathbf{-}\mathbf{75}{\mathbf{e}}^{\mathbf{-}\mathbf{1000}\mathbf{t}}\mathbf{)}\mathbf{(}\mathbf{50}{\mathbf{e}}^{\mathbf{-}\mathbf{1000}\mathbf{t}}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{)}\\ & \mathbf{=}& \mathbf{3}\mathbf{.}\mathbf{75}{\mathbf{e}}^{\mathbf{-}\mathbf{1000}\mathbf{t}}\mathbf{-}\mathbf{3}\mathbf{.}\mathbf{75}{\mathbf{e}}^{\mathbf{-}\mathbf{2000}\mathbf{t}}\end{array}$

The voltage and current at the terminals of the circuit element in Fig 1.5 are zero

for t < 0. For t > 0 they are

a) Find the maximum value of the power delivered to the circuit.

b) Find the total energy delivered to the element

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