# Time for capacitor charging in RLC circuit

Time constant is the time taken by a capacitor to charge to 0.63% of source voltage and in rc circuit time constant is RC. But in series RLC circuit how much time it takes for capacitor to charge to 0.63% of source voltage..?

I searched allover the web and Wikipedia but i didn't find anything. i saw a formula saying that time constant is 2L/R and some where i saw time constant as 1/R*(L/C)1/2.but i don't know it is for inductor(L) or capacitor(C) and how to relate it to capacitor voltage.

• Time constant only applies to first order systems. The time taken to reach 63% of final value in higher order systems has no special significance. – Chu Apr 2 '16 at 7:59

## 2 Answers

At one extreme, RC is exactly what it is for the example without L or a very small value of L. As L becomes more dominant, things change: - So, the blue curve is a small value of L. The pink/magenta curve is the case when the value of L is sufficient to cause a little overshoot and the green condition is when L and C are more dominant than R. It's all about ratios.

This might make useful reading on the topic.

• @Andy aka Hello sir,are they are the voltage waveforms across capacitor only..? if yes in that case it is clear from your information that In under-damping condition there is a peak(overshoot) in voltage across capacitor, and the peak time is the time required for the first peak of the overshoot. is that correct? – Rts11 Apr 2 '16 at 15:23
• That would be the waveform across the capacitor, correct and from a 2V transient step hence it settles down to 2V. – Andy aka Apr 2 '16 at 20:47

An RLC circuit is completely different from an RC. For R = zero, the value of the voltage on C is a sinusoidal even if you feed the RLC with a DC power supply. For values of R which are small compared to L and C, the voltage over C takes a lot of time to stabilize.

Take a look at Wikipedia and at the different "regions" of work, overdamped, critical damped and underdamped.