Parallel RLC circuit

The voltage source .

1. Find the complex number representation of the currents in R,L,C respectively.
   

   

   

   

   

2. Show that the complex number representation of the total current delivered by the voltage source is:
   

   

   

   SOLUTION:

   

   

   where
   

3. The inductor and capacitor resonate when . Show that the total current at resonance is: independent of L & C. So at resonance does any current flow in L & C? Explain. (Derive expressions for the actual currents in R, L & C).
   

   SOLUTION:
   

   At resonance , so .
   

   

   From above:

   

   

   (Note that ).
   

   

   

   at resonance so and have the same amplitude but differ or radians in phase. They add to zero.