Determine the voltage across the capacitor and the current through the inductor:
Using the following formulae, we can easily obtain the voltage across the capacitor and current through an inductor for time t≥0,
${{i}_{L}}(t)=-\sqrt{\frac{C}{L}}{{V}_{c0}}\sin (\frac{1}{\sqrt{LC}}t)u(t)$
${{v}_{C}}(t)={{V}_{c0}}\cos (\frac{1}{\sqrt{LC}}t)u(t)$
Where
${{V}_{co}}=1V\text{ }\therefore \text{Capacitor Initial Voltage}$
Now, let us write Matlab code to compute voltage and current:
%LC Circuit Analysis
clear all;close all;clc
%%Circuit Parameters
L= 100e-3; %Inductance (100mH)
C=10e-6; % Capacitance (10microFarad)
omega_o=1/sqrt(L*C); % Angular Frequency
Vco=1; % Capacitor Initial Voltage
Time=0:1e-5:15e-3; % Time Sampling
Vc=Vco.*cos(omega_o.*Time).*heaviside(Time); % Capacitor Voltage
il=-sqrt(C/L)*Vco.*sin(omega_o.*Time).*... % Inductor Current
heaviside(Time);
%%Plotting Capacitor Voltage and Current
subplot(211)
plot(Time,Vc)
xlabel('Time (s)')
ylabel('Amplitude (V)')
title('V_C')
subplot(212)
plot(Time,il)
xlabel('Time (s)')
ylabel('Amplitude (A)')
title('i_L')
%=============================================
Results:
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