Advertisements
Advertisements
प्रश्न
(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.
उत्तर
(1) Given :
`ε = 200 sin omegat`
`R = 50 Omega`
`ε_0 = 200`
`ε_(av) = ∫_(omegat = 0)^(2pi) (200 sin omegat d (omegat))/(2pi)`
= `(200[-cos (omegat)]_(0)^(2pi))/(2pi)`
= `(-200[cos 2pi - cos 0])/(2pi)`
`ε_(a"v") = 0`
`I_(a"v") = ε_(a"v")/50 = 0/50 = 0 A`
(2) RMS value of EMF
`ε_(RMS) = ε_0/sqrt(2)`
= `200/sqrt(2)`
= `200/1.41 = 141.84 V`
(ii) Two characteristic of resonance in series LCR
(a)At resonance impedance of the current is minimum
Z = R
(b) The net reactance is zero, so the circuit behaves as purely resistive circuit. At resonance frequency peak current is maximum.
APPEARS IN
संबंधित प्रश्न
In a series LCR circuit, obtain the condition under which watt-less current flows in the circuit ?
The figure shows a series LCR circuit with L = 10.0 H, C = 40 μF, R = 60 Ω connected to a variable frequency 240 V source, calculate
(i) the angular frequency of the source which drives the circuit at resonance,
(ii) the current at the resonating frequency,
(iii) the rms potential drop across the inductor at resonance.
A solenoid having inductance 4.0 H and resistance 10 Ω is connected to a 4.0 V battery at t = 0. Find (a) the time constant, (b) the time elapsed before the current reaches 0.63 of its steady-state value, (c) the power delivered by the battery at this instant and (d) the power dissipated in Joule heating at this instant.
The current in a discharging LR circuit without the battery drops from 2.0 A to 1.0 A in 0.10 s. (a) Find the time constant of the circuit. (b) If the inductance of the circuit 4.0 H, what is its resistance?
A series LCR circuit with L = 0.12 H, C = 480 nF, R = 23 Ω is connected to a 230 V variable frequency supply.
(a) What is the source frequency for which current amplitude is maximum. Obtain this maximum value.
(b) What is the source frequency for which average power absorbed by the circuit is maximum. Obtain the value of this maximum power.
(c) For which frequencies of the source is the power transferred to the circuit half the power at resonant frequency? What is the current amplitude at these frequencies?
(d) What is the Q-factor of the given circuit?
Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, C = 27 µF, and R = 7.4 Ω. It is desired to improve the sharpness of the resonance of the circuit by reducing its ‘full width at half maximum’ by a factor of 2. Suggest a suitable way.
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 :
A series LCR circuit containing a 5.0 H inductor, 80 µF capacitors, and 40 Ω resistor is connected to a 230 V variable frequency ac source. The angular frequencies of the source at which power is transferred to the circuit are half the power at the resonant angular frequency are likely to be ______.
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 ______.
