Calculating Voltage Across R and C in Series

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The discussion focuses on calculating the voltage across a resistor (R) and capacitor (C) in series connected to an AC voltage source. The user initially calculated the voltage across the resistor incorrectly due to a mistake in converting capacitance from picofarads to farads. Clarifications were provided regarding the dimensional nature of radians and their role in calculations. Ultimately, the user corrected their conversion error, realizing that the correct capacitance value significantly affected the final voltage result. The importance of careful unit conversion and understanding the relationships in AC circuits is emphasized.
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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
 
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hi themonk! :smile:

(have an omega: ω and try using the X2 icon just above the Reply box :wink:)
themonk said:
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? :smile:

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 :wink:
 
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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.
 
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