Advertisements
Advertisements
प्रश्न
Obtain the expression for the resonant frequency of the LCR series circuit and explain electrical resonance in an LCR series circuit.
Advertisements
उत्तर
- A circuit in which inductance L, capacitance C, and resistance R are connected in series and the circuit admits maximum current corresponding to a given frequency of AC, is called a series resonance circuit.
- The impedance (Z) of an LCR circuit is given by,
Z = `sqrt("R"^2 + (omega"L" - 1/(omega"C"))^2` - At very low frequencies, inductive reactance XL = ωL is negligible but capacitive reactance XC = `1/(omega"L")` is very high.
- As we increase the applied frequency then XL increases and XC decreases.
- At some angular frequency (ωr), XL = XC
i.e., ωrL = `1/(omega_"r""C")`
∴ `(ω_"r")^2 = 1/"LC" "or" (2pi"f"_"r")^2 = 1/"LC"`
∴ `2pi"f"_"r" = 1/sqrt("LC")`
∴ fr = `1/(2pisqrt"LC")`
Where fr is called the resonant frequency. - At this particular frequency fr, since XL = XC we get Z = `sqrt("R"^2 + 0)` = R.
This is the least value of Z. - Thus, when the impedance of an LCR circuit is minimum, the circuit is said to be purely resistive, current and voltage are in phase, and hence the current `"i"_0 = "e"_0/"Z" = "e"_0/"R"` is maximum. This condition of the LCR circuit is called resonance condition and this frequency is called series resonant frequency.
APPEARS IN
संबंधित प्रश्न
In a series LCR circuit at resonance, the applied emf and current are - ______
A parallel LC resonant circuit is used as ______
In the LCR series circuit, what is the condition for current resonance?
A coil of resistance 10 Ω and inductance 100mH and a capacitor of variable capacitance are connected across a 20V, 50Hz A.C. supply. At what capacitance will resonance occur?
A parallel plate air condenser of capacity 10 µF is charged to a potential of 1000 V. The energy of the condenser is ______
Out of the following graphs, which graph shows the correct relation (graphical representation) for LC parallel resonant circuit?
If the potential difference across the inductor (9 mH) is same as that across the condenser (10 µF) in a series R-L-C circuit, then the frequency of the applied e.m.f. is nearly ____________.
In parallel resonance, the current will be minimum, when ____________.
In a resonance tube, first and second resonance positions occur respectively at 28 cm and 88 cm. If the frequency of the fork is 300 Hz, then the speed of sound is ____________.
In LCR circuit, the capacitance is changed from C to 4C. For some resonant frequency, the inductance should be changed from L to ____________.
In rejector circuit, above resonant frequency the circuit is ____________.
In series resonant circuit, at resonance, ____________.
The resonant frequency of a series LCR circuit is 'f'. The circuit is now connected to the sinusoidally alternating e.m.f of frequency '2f'. The new reactance X'L and X'C are related as ____________.
An a.c. source of variable frequency 'f' is connected to an LCR series circuit. Which one of the graphs represent the variation of current 'I' in the circuit with frequency 'f'?
The LCR series and parallel resonant circuits are respectively called as ____________.
An electric lamp connected in series with a capacitor and an AC source glows with a certain brightness. (a) How does the average power change on increasing the capacitance? (b) How does the brightness of the lamp change on increasing the capacitance?
What is an acceptor circuit?
State the use of the acceptor circuit.
A coil of resistance 5 Ω and self inductance 0.2 H is connected in series with variable capacitor across a 30 V(rms), 50 Hz supply. (i) At what capacitance resonance occur? (ii) Find the corresponding current.
In LCR series circuit, the condition for current resonance is ______.
What is a rejector circuit?
What are the Uses of rejector circuit?
A particle starting from extreme position performs S.H.M. The phase difference of the particle between any two successive mean positions is ______.
