The book I am analysis does not get in greater detail of what Resonance within a circuit really is. The only definition I am offered is that of the Resonant Angular Frequency. I beg your pardon is the angular frequency for maximum oscillation.

You are watching: If the value of r is increased, the resonance frequency of this circuit

$$\omega L= \frac1\omega C$$$$ \omega_0 = \frac1\sqrtLC$$

Where l is Inductance and also C is capacitance. I can see here that the resonance relies on the worths for capacitance and inductor"s.

From the definition alone, I"d guess the it"d typical the frequency at which you"re gaining a maximum present when ever the best electro-motive pressure is organized constant.

$$I = \fracEZ $$Where Z is the impedance that the RLC circuit. And also E is EMF max.

So... The present is in ~ it"s max once the Inductance and also Capacitance room both zero. I"d guess the this would median that a circuit would be seen as if just the Resistors room in effect.

But what go this conceptually imply? and when would certainly it issue in use?


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edited Aug 8 "16 at 7:49
moonshineTheleocat
asked Aug 8 "16 in ~ 5:19
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moonshineTheleocatmoonshineTheleocat
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You room incorrect when you say "... The existing is in ~ it"s max once the Inductance and Capacitance space both zero." If the capacitance were zero, the effect would be that you have actually a break in the circuit and no present would flow. If the voltage across the circuit is $V(t) = V_0 \sin(\omega t)$ then for an RLC collection circuit the existing through the circuit is given as $$I(t) = \fracV_0Z \sin (\omega t - \phi)$$ where the impedance, $Z$, is provided as $Z = \sqrtR^2 + (X_L - X_C)^2$, through $X_L = \omega L, X_C = \frac1\omega C$ and $\phi$ is the phase between the current and also the used voltage. For provided vales the $R, L, C$ and varying $\omega$, this has actually a minimum worth of $R$ as soon as $X_L = X_C$ definition a maximum existing will flow. You have the right to determine the resonant frequency indigenous $\omega_0 together = \frac1\omega_0 C$.


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answer Aug 8 "16 at 12:16
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jimjim
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Consider her LCR series circuit as the propelled system and also the power supply together the driveR.The driveR (power supply) will make the current in the driveN device (LCR) oscillate in ~ the frequency the the driveR and these are dubbed forced oscillations.For a resolved amplitude voltage strength supply the an answer (current) in the driveN system depends on the frequency of the driveR.

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At one certain frequency the solution of the driveN device (current) is a maximum this is referred to as resonance and also occurs at the resonant frequency.

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At the resonant frequency the circuit behaves as though the is just a resistor, the impedance that the circuit is equal to the resistance the the resistor, and so the existing in the circuit is the it is provided voltage separated by the resistance the the resistor.

Because it is a series circuit the currents through each that the components are in phase through one another but the voltages throughout them are not, with the voltage throughout the inductor leading the existing by $90^\circ$, the voltage across the resistor in phase through the current and the voltage throughout the capacitor lagging the existing by $90^\circ$.At resonance the voltages across the inductor and the capacitor are equal in magnitude but exactly $180^\circ$ out of phase with one another.The impedance of the inductor $\omega L$ is same to the impedance of the capacitor $\frac1\omega C$. Therefore the it is provided voltage amounts to the voltage across the resistor.

There are countless instances in electronic devices where resonance matters in use and also one instance is a straightforward radio receiver dubbed the crystal set.

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The radio signal is choose up by an aerial and fed right into a tuned circuit comprising an inductor and a capacitor in parallel.If the frequency that the radio signal (driveR) is the same as the the resonant frequency that the tuned circuit (driveN) the voltage at this frequency across capacitor is very big whereas all the other frequency signals picked up by the aerial produce very much smaller voltages across the capacitor and also so space undetected by the remainder of the circuit which convert the radio signal into sound.So the tuned circuit selects the signal from the radio station you wish to listen to and rejects every the other signals. The resonant frequency that the tuned circuit in this circuit is managed by changing the capacitance the the capacitor.