find power and energy delivered

the charge entering the positive terminal of an element is

$\displaystyle q=10\sin{4\ \pi\ t} \ mC$

while the voltage across the element (plus to minus) is

$\displaystyle v=2\cos4\ \pi\ t \ V$

find the power delivered to the element at $\displaystyle t = 0.3s$

so I did thus...

given that $\displaystyle \ v=24.01$

then since $\displaystyle i = \frac{dq}{dt} = \frac{d}{dt}10\sin{4\pi t}

\rightarrow

40 \pi \cos(4 \pi t)$

so at $\displaystyle t=0.3s$ then $\displaystyle i = -101.664$

$\displaystyle p=vi\rightarrow (24.01)(-101.664) = $

its obvioiusly not correct

the correct answer is 164.5mW

so somewhere??? also I didn't know what "plus to minus" meant... AC??

best to multiply the expresions of i(t) and v(t) first

$\displaystyle P(t)=i(t)\,v(t)=80\pi\cos^{2}(4\pi t)\;[\text{mW}].$ Plugging in $\displaystyle t=0.3$ gives the correct result.

$\displaystyle 80\pi\cos^{2}(4\pi 0.3)=164.496 or 164.5 [mW] $ with *wolframalpha*

so it is best to multiply the expresions of i(t) and v(t) first before we apply the t=0.3s

agree about the () just wish this text book would do so it is confusing.. also like the [] around the units.

yes thnks for help...more EE ?? to come (Cool)