# Transient analysis of parallel RLC circuit

Here, I am solving this circuit where Capacitor acts as a voltage source of 10 V. Switch is closed at t=0,and Vc(0-)=10V,I2(0-)=0. When t≥0, what will be the time constant and frequency of the circuit?From my calculation,A=10 and A=B*omega. But how to calculate B? Is omega the angular frequency equal to resonant frequency?I have written the kvl equation I1(t)=dI2/dt Or, Ae^(-kt)cos(wt)=Be^(-kt)wcos(wt)+kBe^(-kt)sin(wt) When t=0, A=Bw and Vc(0-)=10V, hence Vc(t)=10e^(-kt)cos(wt)=I1(t) But what is k and w for parallel RLC circuit? I also got the equation, I1(t)+I2(t)= -dVc(t)/dt Or,Ae^(-kt)cos(wt)+Be^(-kt)sin(wt)=Ae^(-kt)wsin(wt)-Ake^(-kt)cos(wt) By solving it, k= (-1) and B=Aw Correct me if I am wrong.

• To get help with homework questions there is a minimum standard, basically you have to show your work so people can see where you're going wrong and help you.
– K H
Feb 22, 2021 at 8:40
• Hint $v_L(t)=v_C(t)=v_R(t)$ Feb 22, 2021 at 8:45
• I have written the kvl equation I1(t)=dI2/dt Or, Ae^(-kt)cos(wt)=Be^(-kt)wcos(wt)+kBe^(-kt)sin(wt) Feb 22, 2021 at 9:34
• @Camila'svoice Whatever you did you need to add to your question, not in the comments. But, if that's all you did, chances are nobody's going to answer. Feb 22, 2021 at 9:41
• When t=0, A=Bw and as Vc(0-)=10V ,Vc(t)=10e^(-kt)cos(wt) but what's k and w? Feb 22, 2021 at 9:41