Advertisements
Advertisements
प्रश्न
Which of the following combinations should be selected for better tuning of an LCR circuit used for communication?
विकल्प
R = 20 Ω, L = 1.5 H, C = 35µF.
R = 25 Ω, L = 2.5 H, C = 45µF.
R = 15 Ω, L = 3.5 H, C = 30µF.
R = 25 Ω, L = 1.5 H, C = 45µF.
Advertisements
उत्तर
R = 15 Ω, L = 3.5 H, C = 30µF.
Explanation:
Quality factor (Q-factor) of the series resonant circuit:
(i) The characteristic of a series resonant circuit is determined by the quality factor (Q-factor) of the circuit.
(ii) It defines sharpness if i - v curve at resonance when Q-factor is large, the sharpness of resonance curve is more and vice-versa.
(iii) Q-factor is also defined as follows:
Q-factor = `2pi xx "Max energy stored"/"Energy dissipation"`
= `(2pi)/T xx "Max energy stored"/"Mean power dissipated"`
= `"Resonant frequency"/"Bandwidth" = ω_0/(Δω)`
(iv) Q-factor = `V_L/V_R` or `V_C/V_R = (ω_0L)/R` or `1/(ω_0CR)`
⇒ Q-factor = `1/R sqrt(L/C)`
For better tuning of an L-C-R circuit used for communication, quality factor of the circuit must be as high as possible.
We know quality factor should be high for better tuning.
Quality factor (Q) of an L-C-R circuit is `Q = 1/R sqrt(L/C)`
Where R is the resistance, L is the inductance and C is the capacitance of the circuit.
For high Q factor R should be low, L should be high and C should be low.
Important point: Be careful while writing formula for quality factor, this formula we used in this case is only for series L-C-R circuit.
APPEARS IN
संबंधित प्रश्न
A voltage V = V0 sin ωt is applied to a series LCR circuit. Derive the expression for the average power dissipated over a cycle. Under what condition (i) no power is dissipated even though the current flows through the circuit, (ii) maximum power is dissipated in the circuit?
In a series LCR circuit, obtain the condition under which the impedance of the circuit is minimum ?
Show that in an a.c. circuit containing a pure inductor, the voltage is ahead of current by π/2 in phase ?
The magnetic field at a point inside a 2.0 mH inductor-coil becomes 0.80 of its maximum value in 20 µs when the inductor is joined to a battery. Find the resistance of the circuit.
An LR circuit with emf ε is connected at t = 0. (a) Find the charge Q which flows through the battery during 0 to t. (b) Calculate the work done by the battery during this period. (c) Find the heat developed during this period. (d) Find the magnetic field energy stored in the circuit at time t. (e) Verify that the results in the three parts above are consistent with energy conservation.
Using the phasor diagram, derive the expression for the current flowing in an ideal inductor connected to an a.c. source of voltage, v= vo sin ωt. Hence plot graphs showing the variation of (i) applied voltage and (ii) the current as a function of ωt.
A series LCR circuit with R = 20 Ω, L = 1.5 H and C = 35 µF is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?
Keeping the source frequency equal to the resonating frequency of the series LCR circuit, if the three elements, L, C and R are arranged in parallel, show that the total current in the parallel LCR circuit is minimum at this frequency. Obtain the current rms value in each branch of the circuit for the elements and source specified for this frequency.
A coil of 40 henry inductance is connected in series with a resistance of 8 ohm and the combination is joined to the terminals of a 2 volt battery. The time constant of the circuit is ______.
In a series LCR circuit the voltage across an inductor, capacitor and resistor are 20 V, 20 V and 40 V respectively. The phase difference between the applied voltage and the current in the circuit is ______.
In an LCR circuit having L = 8 henery. C = 0.5 µF and R = 100 ohm in series, the resonance frequency in radian/sec is
A series LCR circuit containing 5.0 H inductor, 80 µF capacitor and 40 Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be ______.
As the frequency of an ac circuit increases, the current first increases and then decreases. What combination of circuit elements is most likely to comprise the circuit?
- Inductor and capacitor.
- Resistor and inductor.
- Resistor and capacitor.
- Resistor, inductor and capacitor.
For an LCR circuit driven at frequency ω, the equation reads
`L (di)/(dt) + Ri + q/C = v_i = v_m` sin ωt
- Multiply the equation by i and simplify where possible.
- Interpret each term physically.
- Cast the equation in the form of a conservation of energy statement.
- Integrate the equation over one cycle to find that the phase difference between v and i must be acute.
Draw the phasor diagram for a series LRC circuit connected to an AC source.
Three students, X, Y and Z performed an experiment for studying the variation of ac with frequency in a series LCR circuit and obtained the graphs as shown below. They all used
- an AC source of the same emf and
- inductance of the same value.
- Who used minimum resistance?
- In which case will the quality Q factor be maximum?
- What did the students conclude about the nature of impedance at resonant frequency (f0)?
- An ideal capacitor is connected across 220 V, 50 Hz, and 220 V, 100 Hz supplies. Find the ratio of current flowing through it in the two cases.
In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1 µF and resistance R is 100Ω. The frequency at which resonance occurs is ______.
A 20Ω resistance, 10 mH inductance coil and 15µF capacitor are joined in series. When a suitable frequency alternating current source is joined to this combination, the circuit resonates. If the resistance is made \[\frac {1}{3}\] rd, the resonant frequency ______.
What is true of the current through the resistor, inductor, and capacitor at every instant?
