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 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?
An LR circuit having a time constant of 50 ms is connected with an ideal battery of emf ε. find the time elapsed before (a) the current reaches half its maximum value, (b) the power dissipated in heat reaches half its maximum value and (c) the magnetic field energy stored in the circuit reaches half its maximum value.
Draw a labelled graph showing a variation of impedance of a series LCR circuit with frequency of the a.c. supply.
Derive an expression for the average power dissipated in a series LCR circuit.
The phase diffn b/w the current and voltage at resonance 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 ______.
For an LCR circuit driven at frequency ω, the equation reads
`L (di)/(dt) + Ri + q/C = v_i = v_m` sin ωt
- Multiply the equation by i and simplify where possible.
- Interpret each term physically.
- Cast the equation in the form of a conservation of energy statement.
- Integrate the equation over one cycle to find that the phase difference between v and i must be acute.
Draw the phasor diagram for a series LRC circuit connected to an AC source.
The net impedance of circuit (as shown in figure) will be ______.
When a capacitor is connected in series LR circuit, the alternating current flowing in the circuit ______
