Consider the following RLC circuit Derive the differential e

Consider the following RLC circuit Derive the differential equation of the current i L through the inductor. This is a second order differential equation. Alternately you can use Laplace transform or phasor to do this question. Explain that with R = 1.5K, and L = 100 mh (milli henry), C = 0.01 mu f (0.01 micro farad), this is an overdamped circuit. With L = 100 mh and C = 0.01 mu f, explain if you can change the value of R to make that underdamped or explain that is impossible.

Solution

The series RLC circuit higher than encompasses a single loop with the fast current flowing through the loop being identical for every circuit part. Since the inductive and electrical phenomenon reactance’s XL and XC ar a operate of the availability frequency, the curving response of a series RLC circuit can thus vary with frequency, ƒ. Then the individual voltage drops across every circuit part of R, L and C part are going to be “out-of-phase” with one another as outlined by:

i(t) = Imax sin(t)
The fast voltage across a pure resistance, VR is “in-phase” with the present.
The fast voltage across a pure inductance, VL “leads” the present by 90o
The fast voltage across a pure condenser, VC “lags” the present by 90o
Therefore, VL and VC ar 180o “out-of-phase” and con to every alternative.