How Do You Solve Complex Circuit Problems Involving Capacitors and AC Currents?

[ShadowFX]

So I did a couple circuit questions and these two really have me stumped. One is on paye 613 of The cutnell physics sixth edition number 36. or:

(one star)
A light bulb is connected to a 120.0V wall socket. The current in the bbulb depends on the time t according to the relation I=(0.707 A)sin[(314HZ)t]
a) what is the frequency of the alternating current
b) determine the resistance of the bulb's filament
c) what is the average power consumbed by the light bulb?

from my guesses i believe you use P=I^2R and V/I=R kinds of formulas as well as P=V^2rms/R and P=I^2rmsR to solve bits and pieces but i don't know how to use time and alternating current to deal with this question... in fact i can't even approach this. can someone help me out?

The other question is 92. page 616 (one star)
A 3.00 mF and a 5.00 mF capacitor are connected in series across a 30.0V battery. A 7.0 mF capacitor is then connected in parallel across the 3.00 mF capacitor. Determine the voltage across the 7.00 mF capacitor.

with this question i just generally have no freaking CLUE how to do this other than the capacitors in series and capacitors in parallel equations... i really don't have any idea... help would be appreciated.

 

[ShadowFX]

the second question horrifies me beyond repair... it looks so easy... but it isnt..? series is in reciprocal and parallel is in regular right...?

i think i got a 10V drop on the second question over the 7. but I'm not sure...

 

[ShadowFX]

ok solved the second one... that i thought was harder. can someone help wiht the first? i need to know part b and c.

 

[VinnyCee]

A little help...

For capacitors in series, the Voltage V across each can be found with $$V_1 = \frac{q}{C_1}$$ and these add up to $$30 V = V_1 + V_2$$.

Hope this helps a little