Capacitor and Inductor in Parallel

In summary, to find the equivalent impedance for a circuit with complex impedance, you can use the formula Zeq= 1/[(1/Zc)+(1/ZL)], but it is more commonly expressed as Xeq = 1/[(1/Xc) + (1/XL)], where X represents reactance. Capacitive reactance (Xc) is negative and inductive reactance (XL) is positive.
  • #1

Homework Statement



How do I combine these into an equivalent impedence? I'm dealing with complex impedence, but I'm not sure how to make them into an equivalent impedence.

Homework Equations





The Attempt at a Solution



I guess Zeq= 1/[(1/Zc)+(1/ZL)].
Is this right?
 
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  • #2
Or do I replace the capacitor by an open circuit and inductor by a short?
 
  • #3
swooshfactory said:
I guess Zeq= 1/[(1/Zc)+(1/ZL)].
Is this right?

It looks pretty good to me, however I'd like to clarify a little terminology.

Z represents a complex value called impedance with both real and imaginary parts. Often however it is given as a single number which represents just the magnitude without the angle. As magnitude it is always positive.

Zc & ZL aren't correct because those values are always imaginary with no real part. Instead, the term X is used and it's called reactance.

Capacitive reactance (Xc) is always negative and Inductive reactance (XL) is always positive.

With no real parts the formula would be Xeq = 1/[(1/Xc) + (1/XL)].
 

1. What is the purpose of connecting capacitors and inductors in parallel?

The purpose of connecting capacitors and inductors in parallel is to create a filter circuit that can pass certain frequencies of alternating current while blocking others. This allows for the creation of more complex circuits that can perform specific functions.

2. How do capacitors and inductors behave differently in a parallel circuit compared to a series circuit?

In a parallel circuit, capacitors and inductors behave differently compared to a series circuit because in a parallel circuit, the components have the same voltage across them, while in a series circuit, the components have the same current passing through them. This leads to different equations and behaviors for capacitors and inductors in the two types of circuits.

3. Do capacitors and inductors in parallel interact with each other?

Yes, capacitors and inductors in parallel do interact with each other. This is because they are connected to the same voltage source and therefore affect each other's behavior. The amount of interaction depends on the values of the components and the frequency of the input signal.

4. What is the overall impedance of a parallel circuit with capacitors and inductors?

The overall impedance of a parallel circuit with capacitors and inductors is a combination of the individual impedances of the components. The impedance of a capacitor is inversely proportional to frequency, while the impedance of an inductor is directly proportional to frequency. Therefore, at certain frequencies, the impedance of the capacitor and inductor may cancel each other out, resulting in a lower overall impedance.

5. How can the values of capacitors and inductors in a parallel circuit be chosen to achieve a specific frequency response?

The values of capacitors and inductors in a parallel circuit can be chosen to achieve a specific frequency response by using the formula for the overall impedance of the circuit and solving for the desired frequency. This can be done by adjusting the values of the components or by using a combination of capacitors and inductors to create a bandpass or bandstop filter.

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