Calculating Voltage Across R and C in Series

[themonk]

Homework Statement

A resistor with resistance R and a capacitor with capacitance C are connected in series to an AC voltage source. The time-dependent voltage across the capacitor is given by V$$_{C}$$(t) = V$$_{C_0}$$ sin($$\omega$$*t). (there are no superscripts, but they show up as super for me, though I wanted them to be subscripts)

If R=3 k Ohms , C=100 pF, V$$_{C0}$$=100 mV, and angular frequency $${\omega}$$= 10^5 rad/s, what is V$$_{R}$$?

Homework Equations

$$\frac{V_{C_{0}}{\cdot}R}{\frac{1}{C{\cdot}{\omega}}}$$

The Attempt at a Solution

So I plugged in the variables with 3 k Ohms being 3000 $$\frac{m^{2}*kg}{s*C^{2}}$$, 100 pF being 1E-9 $$\frac{s^{2}*C^{2}}{m^{2}*kg}$$, 100 mV being 1 $$\frac{m^{2}*kg}{C*s^{2}}$$ and 10$$^{5}$$.

When I plugged it all into the equation I got .03 V which is 30 mV*rad. So first there was the problem of the radians being there there is no information about changing it into meters or other useful information. Do I need to use a trig function perhaps?

The hint I was given was : Use the equation obtained in Part B (the equation above) to work out the answer. Be careful of powers of ten in your calculation.

Thank you

 

[tiny-tim]

hi themonk!

(have an omega: ω and try using the X² icon just above the Reply box )

When I plugged it all into the equation I got .03 V which is 30 mV*rad. So first there was the problem of the radians being there there is no information about changing it into meters or other useful information. Do I need to use a trig function perhaps?

mmm … you really like breaking down your https://www.physicsforums.com/library.php?do=view_item&itemid=101", don't you?

radian is dimensionless (metre metre^-1) …

you can just multiply any unit by it, and the result is in the same units

for example, if an object moves with position x = rcosωt, y = rsinωt, its velocity is (-ωrsinωt, ωrcosωt), which looks as if it is in units of metre radians per second, but is in fact only metres per second

 

[themonk]

Thanks tiny-tim for your advice and help! In the end I had converted 100 pF to 1E-9 F rather than 1E-10 so my answer was off by one degree (30 mV vs 3 mV). And I thought the radians would "disappear" somehow, so thanks again.