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

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The discussion revolves around solving two complex circuit problems involving capacitors and AC currents. The first problem requires determining the frequency, resistance, and average power of a light bulb connected to an AC source, with the user unsure how to incorporate time into the calculations. The second problem involves capacitors in series and parallel, where the user initially struggles but eventually finds the voltage across the capacitors. Key formulas mentioned include P=I^2R, V/I=R, and the relationships for capacitors in series and parallel. The user seeks assistance specifically for the first problem after resolving the second.
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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.
 
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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...
 
ok solved the second one... that i thought was harder. can someone help wiht the first? i need to know part b and c.
 
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 :smile:
 

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