parallel rlc voltage source

Question

I am learning about circuits and I have some questions regarding circuit

initial condition: - no initial energy stored before switch is closed - there is current at L1 at t = 0-

I am wondering:

1. at time t= 0+ what is will be the value of Vc? is it 0V or Vs?
2. If it is 0V, why? Because it will not satisfy the KVL eqn when switch is closed.
3. If it is Vs, why so? I understand that Voltage at L can change instatenously but not voltage at C and R. that means at t=0+, should not the VR, C1 and VR2= 0 V? but again this will violates KVL law.

Answer 1

Use the Laplace transform. Several forms of the voltage across the parallel combination are possible, depending on component values. But this voltage is always zero at t=0

If the system is underdamped, this voltage is an exponentially decaying sine term, hence equal to zero at t=0

If the system is overdamped, the voltage is the difference of two exponentials and, again, zero at t=0

For equal roots, the voltage is of the form \$te^{-at}\$, so equal to zero at t=0

The above assumes that all component values are non-zero, and zero initial conditions. You're question is contradictory on initial conditions - 'no energy storage' and 'there is current in L1 at t=0- '