Series RC and parallel RC

[adityapratapa]

Given : a series RC circuit with Rs and Cs and Parallel circuit with Rp and Cp...also given both are equivalent and Q-factor is high. Calculate the range of w for both circuits are equivalent.


pls help asap...

 

[NascentOxygen]

Determine the impedance of the second circuit, expressing it as a REAL component and an IMAGINARY component.

 

[tiny-tim]

welcome to pf!

hi adityapratapa! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[adityapratapa]

hi adityapratapa! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

i got it till this..

Rs=Rp/(1+Q^2) and Cp=Cs(1+1/Q^2) assuming Q=1/wRsCs=wRpCp...but when it comes to finding the range of w I'm struck...

 

[DeeNos]

I would like to clarify that Rs and Cs refer to the resistance and capacitance values in the series RC circuit, while Rp and Cp refer to the same values in the parallel RC circuit.

Given that both circuits are equivalent and have a high Q-factor, we can assume that the impedance of the series RC circuit is equal to the admittance of the parallel RC circuit. This means that the range of w (angular frequency) for both circuits to be equivalent would be when the impedance and admittance are equal.

To calculate this range, we can use the formula for impedance in a series RC circuit, Z = √(R^2 + (1/wC)^2), and the formula for admittance in a parallel RC circuit, Y = (1/Rp) + jwCp.

Setting these two equations equal to each other and solving for w, we get w = 1/√(LC). This means that the range of w for both circuits to be equivalent is when the angular frequency is equal to 1/√(LC).

In conclusion, the range of w for both series RC and parallel RC circuits to be equivalent is when the angular frequency is equal to 1/√(LC), where L is the inductance of the circuit and C is the capacitance.