Resonance of a Parallel LCR network

In summary, a parallel LCR network is a type of electrical circuit that consists of an inductor, capacitor, and resistor connected in parallel. When an AC voltage is applied to the circuit, the inductor and capacitor exchange energy continuously, leading to a phenomenon called resonance. At resonance, the circuit exhibits a high impedance, causing the current to be at its maximum and the voltage to be at its minimum. This phenomenon has important applications in various electronic devices, such as filters and amplifiers.
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nathangrand
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Why does the resonance peak of a parallel LCR network (capacitor in parallel with in-series inductor and resisitor) get smaller in amplitude with increasing resistance? I have impedance/DC resistance plotted against frequency.


I'm really not sure about how to go about showing this, preferably mathematically. At resonance is the reactance 0, implying the impedance is just the resistance?

Also, what is the correct expression for the resonant frequency of this circuit? I get w[tex]^{2}[/tex] = w0[tex]^{2}[/tex] - y[tex]^{2}[/tex] when y=R/2L and w0= 1/ [tex]\sqrt{LC}[/tex] but I've seen different expressions, such as under other configurations here http://en.wikipedia.org/wiki/RLC_circuit

Any help would be massively appreciated!
 
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1. What is a Parallel LCR network?

A Parallel LCR (Inductance, Capacitance, Resistance) network is a type of electrical circuit that consists of a combination of inductors, capacitors, and resistors connected in parallel. This type of network is commonly used in electronic devices such as radios, televisions, and computers.

2. What is resonance in a Parallel LCR network?

Resonance in a Parallel LCR network occurs when the inductive reactance (XL) and capacitive reactance (XC) cancel each other out, resulting in a purely resistive circuit. This leads to a significant increase in the circuit's current and a decrease in its overall impedance.

3. How is the resonant frequency of a Parallel LCR network calculated?

The resonant frequency of a Parallel LCR network can be calculated using the formula f=1/(2π√(LC)), where f is the resonant frequency in hertz, L is the inductance in henries, and C is the capacitance in farads.

4. What are the applications of resonance in a Parallel LCR network?

Resonance in a Parallel LCR network has various applications, such as in tuning circuits, bandpass filters, and frequency-selective networks. It is also used in radio frequency (RF) circuits to select a specific frequency for transmission or reception.

5. What happens to the impedance at resonance in a Parallel LCR network?

At resonance, the impedance of a Parallel LCR network is at its minimum value, which is equal to the resistance (R) of the circuit. This means that the circuit is more efficient at transferring energy, and there is less power loss due to impedance.

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