Advertisements
Advertisements
Question
In series LCR circuit, the plot of Imax vs ω is shown in figure. Find the bandwidth and mark in the figure.
Advertisements
Solution
We know that bandwidth = (ω2 – ω1).
Where ω1 and ω2 are two frequencies where the current amplitude of LCR circuit becomes `12sqrt(12)` times (i.e., Irms) the value of current is maximum at resonant frequency.
`I = E_0/sqrt(2) = 1/sqrt(2)` = 0.707 Amp
From graph ω1 and ω2 at 0.707A current is 0.8 and 1.2 rad/sec.
So Bandwith ω2.ω1 = 1.2 – 0.8 = 0.4 rad/sec.
APPEARS IN
RELATED QUESTIONS
A series LCR circuit is connected across an a.c. source of variable angular frequency 'ω'. Plot a graph showing variation of current 'i' as a function of 'ω' for two resistances R1 and R2 (R1 > R2).
Answer the following questions using this graph :
(a) In which case is the resonance sharper and why?
(b) In which case in the power dissipation more and why?
In a series LCR circuit, obtain the condition under which watt-less current flows in the circuit ?
A coil of resistance 40 Ω is connected across a 4.0 V battery. 0.10 s after the battery is connected, the current in the coil is 63 mA. Find the inductance of the coil.
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.
Answer the following question.
Draw the diagram of a device that is used to decrease high ac voltage into a low ac voltage and state its working principle. Write four sources of energy loss in this device.
In an LCR series a.c. circuit, the voltage across each of the components, L, C and R is 50V. The voltage across the LC combination will be ______.
Assertion: When the frequency of the AC source in an LCR circuit equals the resonant frequency, the reactance of the circuit is zero, and so there is no current through the inductor or the capacitor.
Reason: The net current in the inductor and capacitor is zero.
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
Draw the phasor diagram for a series LRC circuit connected to an AC source.
When an alternating voltage of 220V is applied across device X, a current of 0.25A flows which lags behind the applied voltage in phase by π/2 radian. If the same voltage is applied across another device Y, the same current flows but now it is in phase with the applied voltage.
- Name the devices X and Y.
- Calculate the current flowing in the circuit when the same voltage is applied across the series combination of X and Y.
A series LCR circuit is connected to an ac source. Using the phasor diagram, derive the expression for the impedance of the circuit.
Draw a labelled graph showing variation of impedance (Z) of a series LCR circuit Vs frequency (f) of the ac supply. Mark the resonant frequency as f0·
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.
When a capacitor is connected in series LR circuit, the alternating current flowing in the circuit ______
Out of the following which one is NOT the characteristic of LCR series resonant circuit?
What constitutes a series LCR circuit?
What is true of the current through the resistor, inductor, and capacitor at every instant?
