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$$
\text { The voltage and current at the terminals of an electrical element are }
$$

$$
\begin{aligned} v &=50 e^{-1600 t}-50 e^{-400 t} \mathrm{V} \\ i &=5 e^{-1600 t}-5 e^{-400 t} \mathrm{mA} \end{aligned}
$$

$$
\begin{array}{l}{\text { a) Find the power at } t=625 \mu \mathrm{s} \text { . }} \\ {\text { b) How much energy is delivered to the circuit element between } 0 \text { and } 625 \mu \mathrm{s} \text { ? }}\end{array}
$$

$$
P(t)=V(t) I(t)=[50e^{-1600t}-50e^{-400t}][5e^{-1600t}-5e^{-400t}]
$$

$$
P[625 \mu s]=P[625*10^{-6}s]=[sub \ t=625*10^{-6}][sub \ t=625*10^{-6}]
$$

$$
P[625 \mu s]=42.2 mw
$$

$$
W(t)=\int^{625*10^{-6}}_{0} V(t)I(t) dt=\int^{625*10^{-6}}_{0}[50e^{-1600 t}-50e^{-400t}][5e^{-1600t}-5e^{-400t}]
$$

$$
W_{0\rightarrow625 \mu s} =12.14 \mu J
$$

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