How to Find the Voltage Across a Capacitor in an RLC Circuit?

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To find the voltage across a capacitor in an RLC circuit, use the equation V(t) = i(t)R + (1/C) ∫_0^t i(u)du + L di(t)/dt, as per Kirchhoff's laws. If the circuit is powered by a constant voltage source, the capacitor voltage will equal the battery voltage after a sufficient time. For alternating current sources, the same equation applies, but requires solving for specific conditions. The configuration of the components, whether in series or parallel, affects the calculations. Understanding these principles is essential for analyzing RLC circuits effectively.
dancingmonkey
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My question is how do I find the voltage across a capacitor? I have an RLC circuit with a switch and battery. It only gives me the values for the battery, L, C, and R.

My main question is, is there an equation or something to find the voltage across a capacitor?
 
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Is it connected in series? If so, according to Kirchhoff, V(t) = i(t)R + (1/C) int_0^t i(u)du + L di(t)/dt

Solve that equation and you are done.
 
If the battery is a constant voltage source (direct current), the voltage across the capacitor should be that voltage if you wait a sufficiently long time (typically a few seconds will do the trick, if the inductance is not too high).

If it is an alternating current source, you will have to solve the equation posted by Termotanque.
 

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