How is the equation for impedance in a parallel resonance LC circuit derived?

In summary, according to the theory of RLC circuits, at resonance frequency the circuit impedance is at its maximum value. This impedance is resistive and its value is determined by the ratio of the inductance and the product of capacitance and resistance (L/Cr). The exact derivation of this equation may not be explicitly explained in all resources, but it can be found in various sources such as the one provided above.
  • #1
uzair_ha91
92
0
"At resonance frequency, the circuit impedance is maximum. It is resistive and its value is given L/Cr..."
The book doesn't explain how impedance equals L/Cr, so I'm confused here. How is it derived? (Can you please show all the steps?)
Thanking in advance...
 
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  • #2
uzair_ha91 said:
"At resonance frequency, the circuit impedance is maximum. It is resistive and its value is given L/Cr..."
The book doesn't explain how impedance equals L/Cr, so I'm confused here. How is it derived? (Can you please show all the steps?)
Thanking in advance...

This resource should help you out:

http://en.wikipedia.org/wiki/RLC_circuit

.
 
  • #3
Sorry , the article does not have that equation nor any explanation regarding that...
 

1. What is a parallel resonance LC circuit?

A parallel resonance LC circuit is a type of electrical circuit that consists of a capacitor and an inductor connected in parallel. It is also known as a tank circuit because it can store and release energy like a tank.

2. How does a parallel resonance LC circuit work?

In a parallel resonance LC circuit, the capacitor and inductor work together to create a resonant frequency. At this frequency, the circuit becomes highly reactive, causing the voltage across the capacitor and current through the inductor to reach their maximum values. This results in a high amount of energy being stored in the circuit.

3. What is the resonant frequency of a parallel resonance LC circuit?

The resonant frequency of a parallel resonance LC circuit is determined by the values of the capacitor and inductor. It can be calculated using the formula: f = 1/(2π√(LC)), where f is the resonant frequency in Hertz, L is the inductance in Henrys, and C is the capacitance in Farads.

4. What are the applications of parallel resonance LC circuits?

Parallel resonance LC circuits have various applications in electronic devices, such as in radio tuners, filters, and oscillators. They are also used in power systems for power factor correction and in wireless charging systems.

5. How does changing the values of the capacitor and inductor affect a parallel resonance LC circuit?

The resonant frequency of a parallel resonance LC circuit is directly affected by the values of the capacitor and inductor. Increasing the capacitance will decrease the resonant frequency, while increasing the inductance will increase the resonant frequency. Changing these values can also affect the amount of energy stored in the circuit and the frequency response of the circuit.

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