Sinusoidal Response of RC Circuit

Sinusoidal Response of RC Circuit:

Consider a Sinusoidal Response of RC Circuit consisting of resistance and capacitance in series as shown in Fig. 12.18.

Sinusoidal Response of RC Circuit

The, switch, S, is closed at t = 0. At t = 0, a sinusoidal voltage V cos (ωt + θ) is applied to the RC Circuit, where V is the amplitude of the wave and θ is the phase angle. Applying Kirchhoff’s voltage law to the circuit results in the following differential equation.

The complementary function

The particular solution can be obtained by using undetermined coefficients.

Sinusoidal Response of RC Circuit

Substituting Eqs 12.27 and 12.28 in Eq. 12.25, we get

Sinusoidal Response of RC Circuit

Comparing both sides,

From which,

Sinusoidal Response of RC Circuit

Substituting the values of A and B in Eq. 12.27, we have

Sinusoidal Response of RC Circuit

Putting

To find M and Φ, we divide one equation by the other,

Sinusoidal Response of RC Circuit

Squaring both equations and adding, we get

Sinusoidal Response of RC Circuit

The particular current becomes

The complete solution for the current i = ic + ip

Sinusoidal Response of RC Circuit

Since the capacitor does not allow sudden changes in voltages at t = 0, i = V/R cos θ

Sinusoidal Response of RC Circuit

The complete solution for the current is

Sinusoidal Response of RC Circuit

Updated: February 13, 2020 — 9:33 pm