LC Parallel Circuit with current source in steady state
Inductor

For a steady state applied current, an inductor behaves like a short circuit because: -

$$V = L\dfrac{di}{dt}$$

If the current is steady state it is not changing hence di/dt = 0 therefore V must be zero and the inductor looks like a short circuit..

However, if the voltage is constant, then di/dt has a non-zero value hence current rises with respect to time.



Capacitor

For a steady state applied voltage, a capacitor behaves like an open circuit because: -

$$I = C\dfrac{dv}{dt}$$

If the voltage is constant then the current has to be zero hence it looks like an open circuit.

However, if the current is constant, then dv/dt has a non-zero value hence the voltage rises with respect to time.




  LC Parallel Circuit with current source in steady state


In this scenario the steady state situation is that all the current flows through the inductor and the capacitor never charges.