Parallel RLC Circuit: Using General Impedance Equation

[wetwilly92]

Quick Question...

Given:

Can I still use the general impedance equation for parallel RLC circuits even though the resistors are not in parallel with the other components? Substituting the two resistors for a single resistor with the equivalency resistance?

 

[technician]

The first leg is (Rc and C in series) and this combination is in parallel with (Rl and L in series)

 

[wetwilly92]

The first leg is (Rc and C in series) and this combination is in parallel with (Rl and L in series)

Does this give us...

1) Q²/C - I_CR_C - V = 0
2) I_LR_L - (L * di_L/dt) - V = 0

Or am I just completely off?

 

[technician]

The circuit is an AC circuit so you need to use Reactance of C... Xc =1/ωC to get an expression for the impedance of the Rc C arm.
You need to use Xl = ωL to get an expression for the Impedance of the Rl L arm
The overall impedance is these 2 impedances in parallel.

 

[asteriatic]

Yes, you can still use the general impedance equation for parallel RLC circuits by substituting the two resistors for a single resistor with the equivalent resistance. This is because the general impedance equation takes into account the overall resistance in the circuit, regardless of how it is connected. In parallel circuits, the total resistance is equal to the reciprocal of the sum of the reciprocals of the individual resistances. Therefore, replacing multiple resistors with a single equivalent resistor will not affect the overall resistance in the circuit and the general impedance equation can still be used.