Basic Circuit Capacitor/Resistor Question

[jlv11203]

Homework Statement

A 1.0 micro Farads capacitor is connected in series with a 16 Ohms resistor as shown in the figure. If the voltage across the capacitor is Vc(t) = 18 cos(1000t) V, what is the voltage across the resistor, VR, at t = 1 s?

Note: The voltage frequency is in radians per second.

----Capacitor--------Resistor-----black box----

the ends are connected in the picture given, eg: black box connected back to capacitor

Homework Equations

V_c = 10*cos(1000t)
i_c = C dv/dt

The Attempt at a Solution

My professor was absent from class the day we were supposed to learn this, but the homework is still due in a couple days. Honestly, I'm not really sure where to start. I would think the current in the branch with the capacitor and resistor would need to be found, in order to find the voltage drop across the resistor. Any nudges in the right direction or help would be greatly appreciated!

 

[MATLABdude]

For a question like this, you need to firstly determine whether the response is steady state, or transient. HINT: Does $\tau=RC$ ring a bell? If not, the Wikipedia article on http://en.wikipedia.org/wiki/RC_time_constant" . Now, how does that compare to the frequency of the voltage source?

EDIT: ...And welcome to PhysicsForums!

 

[jlv11203]

We have not talked about anything regarding capacitors in class yet, let alone time constants. I vaguely remember them from a physics class I took last year, but I was able to figure out the solution to this problem after re-reading the chapter in the book...it ends up I was over-complicating it

This is what I figured out:

use i = C dv/dt to find the current through the capacitor at t = 1s. i= 1*10^-6 * d/dt (18*cos(1000t)), then, apply Ohm's law to the resistor since the current in that branch is the same throughout: v = ir, v = i * 16.

Thanks for the help and the welcome! :)

ps: that link is coming in very useful for the other questions on the assignment!