Advertisements
Advertisements
प्रश्न
Derive an expression for the average power consumed in a series LCR circuit connected to a.c. source in which the phase difference between the voltage and the current in the circuit is Φ.
Advertisements
उत्तर
Power in ac circuit
Voltage v in an ac circuit is:
`v =v_m sinomegat`
which drives through the circuit a current i
i = im sin (ωt +Φ), where`i_m =v_m/Z`and
`phi =tan^-1 ((X_c -X_L)/R)`
Power `p = v_i = (v_msin omegat)[i_m sin(omegat +phi)]`
`=(v_mi_m)/2 [cosphi - cos[2omegat +phi]]`
Calculating the average power, it is observed that the average of the term
cos (2ωt + Φ) is equal to zero.
Thus,
Average power,
`p = (v_mi_m)/2 cosphi = VI cos phi`
APPEARS IN
संबंधित 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?
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.
(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.
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.
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.
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
If the rms current in a 50 Hz ac circuit is 5 A, the value of the current 1/300 seconds after its value becomes zero is ______.
Select the most appropriate option with regard to resonance in a series LCR circuit.
The net impedance of circuit (as shown in figure) will be ______.
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 ______.
