Question 8.24: The circuit in Figure P8-24 is operating in the sinusoidal s......
The circuit in Figure P8-24 is operating in the sinusoidal steady state with i_{\mathrm{S}}(t)=I_{\mathrm{A}} \cos (\omega t).
Derive general expressions for the steady-state responses \rm{V}_{\mathrm{R}} \text { and } \rm{I}_{\mathrm{C}}.
This problem can be solved by using current division in the phasor domain. The following MATLAB code presents the required calculations.
Script File
clear all
syms w C R positive
syms IA IC IR VR Is ZC
% Create the source current
Is = IA*exp(0*j*pi/180);
% Create the capacitor impedance
ZC = 1/j/w/C;
% Use current division to find the two currents in the circuit
IC = simplify(Is/ZC/(1/ZC + 1/(R+R)))
IR = Is/(R+R)/(1/ZC + 1/(R+R));
% Apply Ohm's Law to find the output voltage
VR = simplify(R*IR)
% Check KCL
CheckKCL = simplify(Is-IC-IR)
IC =
2*i*IA*w*C*R/(2*i*w*C*R+1)
VR =
IA*R/(2*i*w*C*R+1)
CheckKCL =
0
\begin{aligned}& \mathbf{V}_{\mathrm{R}}=\frac{R I_{\mathrm{A}}}{1+2 j \omega R C}\\ \\& \mathbf{I}_{\mathrm{C}}=\frac{2 j \omega R C I_{\mathrm{A}}}{1+2 j \omega R C}\end{aligned}