24P2Q04

4a)

$\displaystyle \omega =\frac{2\pi }{T}=\frac{2\pi }{0.040}=157\text{ rad }{{\text{s}}^{-1}}$

$\displaystyle \begin{aligned}V&={{V}_{\max }}\sin \omega t \\V&=4.8\sin 157t \\ \end{aligned}$

4bi)

$\displaystyle \begin{aligned}\text{Total resistance}&=12+6\parallel 6 \\&=12+3 \\&=15\text{ }\!\!\Omega\!\!\text{ } \\ \end{aligned}$

4bii)

$\displaystyle \begin{aligned}\left\langle P \right\rangle &=\frac{1}{2}\frac{{{V}_{pk}}^{2}}{2} \\&=\frac{1}{2}\frac{{{4.8}^{2}}}{2} \\&=0.768\text{ W} \end{aligned}$

4biii)

By P.D.P.
$\displaystyle \frac{3}{12+3}\times 4.8=0.96\text{ V}$

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24P2Q04

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