Question $1(60$ marks$)$

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$($a$)$

Referring to Fig. $1($a$),$ calculate $($i$)$ the frequency f$0$ at which the maximum power is dissipated in the load $($comprising R$,$ L and C$)$ and $($ii$)$ the average sinusoidal steady$-$state power dissipated in the load at that frequency.

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Figure $1($a$)$

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R$1=(560+$ $),$ R $=10,$ C $=(1000+$ $)$ pF$,$ L $=(1000+$ $)$ nH and Vs is a sinusoid with an amplitude of $1$ V$.$

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f$0$

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$5\mathrm{.}023$mHz

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Pload at f$0$

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$1\mathrm{.}5$E$-5$W

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SPICE circuit schematic

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SPICE output