I0=V/RR=(xL-xc)/tan\phiPAv=1/2VI0cos\phiMax Current in RLC Circuit @ 1759 Hz

In summary, at the resonant frequency of 2,459 Hz for an RLC circuit with a capacitance of 3 micro-Farads, the average power dissipated by the circuit is 74 Watts when connected to a voltage source with a maximum voltage of 58 volts. At a frequency of 1,759 Hz, the maximum current is 2.14 amps. To find the value of the resistor, we can use the formula I0=V/R and since the reactive impedances cancel each other at resonance, the average power dissipated by the resistor will be equal to the 74 Watts given. Therefore, the value of the resistor can be found by dividing the maximum voltage of 58 volts by the maximum current
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Homework Statement


At resonant frequency of 2,459 Hz for an RLC circuit, average power of circuit is 74 Watts when connected to a voltage source with a maximum voltage of 58 volts. If capacitance is 3 micro-Farads, what is maximum current, in amps, at 1,759 Hz? Answer is 2.14.

Homework Equations


I0=V/R
R=(xL-xc)/tan[tex]\phi[/tex]
PAv=1/2VI0cos[tex]\phi[/tex]
xL=[tex]\omega[/tex]L
xc=1/[tex]\omega[/tex]c
f0=1/(2[tex]\pi[/tex][tex]\sqrt{}LC[/tex])

The Attempt at a Solution


L=1/(2[tex]\pi[/tex])2[/SUPf02c
 
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  • #2
You've attempted to find the value of the inductor. What value did you get?

Can you find the value of the resistor? (Hint: at resonance the reactive impedances cancel each other, and the average power given will be dissipated by the resistor. What's the average power dissipated by a resistor given a maximum value for the voltage?).
 
  • #3
I appreciate your assistance!
 

FAQ: I0=V/RR=(xL-xc)/tan\phiPAv=1/2VI0cos\phiMax Current in RLC Circuit @ 1759 Hz

How do I calculate the maximum current in an RLC circuit?

The maximum current in an RLC circuit can be calculated using the formula I0=V/RR=(xL-xc)/tan\phiPAv=1/2VI0cos\phiMax, where V is the voltage across the circuit, R is the resistance, xL is the inductive reactance, and xc is the capacitive reactance. This formula takes into account the phase angle, which represents the difference in phase between the voltage and current in the circuit.

What is the significance of the frequency 1759 Hz in this equation?

The frequency of 1759 Hz is used because it is the resonant frequency of the RLC circuit. At this frequency, the inductive and capacitive reactances cancel each other out, resulting in a maximum current in the circuit.

What is the difference between RLC circuits and other types of circuits?

RLC circuits are composed of a resistor (R), an inductor (L), and a capacitor (C). These components create a resonant circuit that can amplify certain frequencies and dampen others. This is different from other types of circuits, such as RC circuits or RL circuits, which only contain two of these components.

How do I determine the phase angle in an RLC circuit?

The phase angle in an RLC circuit can be determined by using the equation tan\phi=xc-xL/R, where xc is the capacitive reactance and xL is the inductive reactance. This formula takes into account the difference in phase between the voltage and current in the circuit.

What factors can affect the maximum current in an RLC circuit?

The maximum current in an RLC circuit can be affected by various factors such as the value of the resistance, the inductance and capacitance of the components, and the frequency of the input voltage. These factors can change the reactance values and therefore impact the overall current in the circuit.

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