Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
he variation of current with angular frequency for the two resistances R1 and R2 is shown in the graph below.
Here,
i = Virtual current through the circuit
ω = Angular frequency of the source
ωr = Resonance frequency
From the graph, we can see that resonance for the resistance R2 is sharper than for R1 because resistance R2 is less than resistance R1. Therefore, at resonance, the value of peak current will rise more abruptly for a lower value of resistance.
b) Power associated with the resistance is given by
P=Ev Iv
where
Ev = Virtual voltage
Iv = Virtual current
From the graph, we can say that the virtual current in case of R2 is more than the virtual current in case of R1. Hence, the power dissipation in case of the circuit with R2 is more than that with R1.
APPEARS IN
संबंधित प्रश्न
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.
The potential difference across the resistor is 160V and that across the inductor is 120V. Find the effective value of the applied voltage. If the effective current in the circuit be 1.0 A, calculate the total impedance of the circuit.
Draw a labelled graph showing a variation of impedance of a series LCR circuit with frequency of the a.c. supply.
In a series LCR circuit supplied with AC, ______.
In series combination of R, L and C with an A.C. source at resonance, if R = 20 ohm, then impedence Z of the combination is ______.
The resonant frequency of a RF oscillator is 1 MHz and its bandwidth is 10 kHz. The quality factor will be :
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 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.
Which of the following statements about a series LCR circuit connected to an ac source is correct?
A series LCR circuit (L = 10 H, C = 10 µF, R = 50 Ω) is connected to V = 200 sin (100t). If ν0 is the resonant frequency and ν is the source frequency, then ______.
