Can the Impedance of Series RC and Parallel RL Circuits be Equal with Same R?

In summary, the question asks whether a series RC circuit and a parallel RL circuit can have the same impedance if the resistance (R) is the same in both. The equations for impedance in each type of circuit are Zr=R, Zc=1/iwC, and ZL=iwL. With three unknowns and two equations, it is necessary to equate the real and imaginary components of the two Z's and solve for L and C, if possible. The physical explanation for this phenomenon is not immediately obvious.
  • #1
phantomfx8192
1
0

Homework Statement


Can a series RC circuit and a parallel RL circuit have the same impedance if the R is the same in both? What would the values of R, L and C have to be if they can? Why/why not, physically speaking?

Homework Equations


Zr=R
Zc=1/iwC
ZL=iwL

The Attempt at a Solution


I know in series the total impedance is the square root of each of the involved impedances squared, and if it's in parallel then it is the product of the two impedances divided by the square root of each of the involved impedances squared. So I have the two equations for impedance, but three unknowns and I'm not sure where to go next. Also, I have no intuition as to physically why or why not this statement would be true.
 
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  • #2
phantomfx8192 said:

Homework Statement


Can a series RC circuit and a parallel RL circuit have the same impedance if the R is the same in both? What would the values of R, L and C have to be if they can? Why/why not, physically speaking?



Homework Equations


Zr=R
Zc=1/iwC
ZL=iwL


The Attempt at a Solution


I know in series the total impedance is the square root of each of the involved impedances squared, and if it's in parallel then it is the product of the two impedances divided by the square root of each of the involved impedances squared. So I have the two equations for impedance, but three unknowns and I'm not sure where to go next. Also, I have no intuition as to physically why or why not this statement would be true.

Z of series R-C is R - j/wC.
Y of parallel R-L is G - j/wL and Z =1/Y.

Equate the real and the imaginary components of the two Z's and see if there is a solution for L vs. C for any frequency w.
 

Related to Can the Impedance of Series RC and Parallel RL Circuits be Equal with Same R?

1. What is the difference between RL and RC circuit impedance?

RL and RC circuit impedance refer to the overall opposition to current flow in an electrical circuit. The main difference between the two is that RL (resistor-inductor) circuits only contain resistors and inductors, while RC (resistor-capacitor) circuits only contain resistors and capacitors.

2. How is impedance calculated in an RL circuit?

In an RL circuit, impedance (Z) is calculated using the formula Z = √(R^2 + XL^2), where R is the resistance and XL is the inductive reactance. XL is calculated using the formula XL = 2πfL, where f is the frequency of the alternating current and L is the inductance of the circuit.

3. How does capacitance affect impedance in an RC circuit?

In an RC circuit, capacitance (C) affects impedance by decreasing it as the frequency of the alternating current increases. This is because as the frequency increases, the reactance of the capacitor (XC) decreases, resulting in a lower impedance value.

4. Can impedance be used to determine the phase relationship between voltage and current in an RL or RC circuit?

Yes, impedance can be used to determine the phase relationship between voltage and current in an RL or RC circuit. In an RL circuit, the current lags behind the voltage by 90 degrees, while in an RC circuit, the current leads the voltage by 90 degrees.

5. How does impedance affect the power dissipation in an RL or RC circuit?

Impedance affects the power dissipation in an RL or RC circuit by limiting the flow of current, resulting in less power being dissipated. This is because as impedance increases, the voltage drop across the circuit also increases, reducing the amount of power available to the components in the circuit.

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