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
In a series LCR circuit, VL = VC ≠ VR. What is the value of power factor?
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?
Why does current in a steady state not flow in a capacitor connected across a battery? However momentary current does flow during charging or discharging of the capacitor. Explain.
A source of ac voltage v = v0 sin ωt, is connected across a pure inductor of inductance L. Derive the expressions for the instantaneous current in the circuit. Show that average power dissipated in the circuit is zero.
A series LCR circuit is connected to an ac source. Using the phasor diagram, derive the expression for the impedance of the circuit. Plot a graph to show the variation of current with frequency of the source, explaining the nature of its variation.
A coil having an inductance L and a resistance R is connected to a battery of emf ε. Find the time taken for the magnetic energy stored in the circuit to change from one fourth of the steady-state value to half of the steady-state value.
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.
(i) An a.c. source of emf ε = 200 sin omegat is connected to a resistor of 50 Ω . calculate :
(1) Average current (`"I"_("avg")`)
(2) Root mean square (rms) value of emf
(ii) State any two characteristics of resonance in an LCR series circuit.
Answer the following question.
In a series LCR circuit connected across an ac source of variable frequency, obtain the expression for its impedance and draw a plot showing its variation with frequency of the ac source.
Use the expression for Lorentz force acting on the charge carriers of a conductor to obtain the expression for the induced emf across the conductor of length l moving with velocity v through a magnetic field B acting perpendicular to its length.
Derive an expression for the average power dissipated in a series LCR circuit.
In an L.C.R. series a.c. circuit, the current ______.
In series LCR circuit, the phase angle between supply voltage and current is ______.
At resonance frequency the impedance in series LCR 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
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.
A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3 kΩ, an inductor of inductive reactance XL = 250 πΩ, and an unknown capacitor. The value of capacitance to maximize the average power should be ______.
A series RL circuit with R = 10 Ω and L = `(100/pi)` mH is connected to an ac source of voltage V = 141 sin (100 πt), where V is in volts and t is in seconds. Calculate
- the impedance of the circuit
- phase angle, and
- the voltage drop across the inductor.
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.
Which of the following combinations should be selected for better tuning of an L-C-R circuit used for communication?
