Advertisements
Advertisements
प्रश्न
In a series LCR circuit, obtain the condition under which watt-less current flows in the circuit ?
Advertisements
उत्तर
Average power dissipated through a series LCR circuit is given by \[P_{av} = E_v I_v \cos\left( \phi \right)\]
where, Ev = rms value of alternating voltage
Iv = rms value of alternating current
Φ = phase difference between current and voltage
For wattless current, the power dissipated through the circuit should be zero.
\[i . e . , \cos\left( \phi \right) = 0\]
\[ \Rightarrow \phi = \frac{\pi}{2}\]
Hence, the condition for wattless current is that the phase difference between the current and voltage should be π/2 and the circuit is purely inductive or purely capacitive.
APPEARS IN
संबंधित प्रश्न
Why does current in a steady state not flow in a capacitor connected across a battery? However momentary current does flow during charging or discharging of the capacitor. Explain.
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.
Two coils A and B have inductances 1.0 H and 2.0 H respectively. The resistance of each coil is 10 Ω. Each coil is connected to an ideal battery of emf 2.0 V at t = 0. Let iA and iBbe the currents in the two circuit at time t. Find the ratio iA / iB at (a) t = 100 ms, (b) t = 200 ms and (c) t = 1 s.
Answer the following question.
In a series LCR circuit connected across an ac source of variable frequency, obtain the expression for its impedance and draw a plot showing its variation with frequency of the ac source.
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.
Keeping the source frequency equal to the resonating frequency of the series LCR circuit, if the three elements, L, C and R are arranged in parallel, show that the total current in the parallel LCR circuit is minimum at this frequency. Obtain the current rms value in each branch of the circuit for the elements and source specified for this frequency.
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?
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 ______.
At resonance frequency the impedance in series LCR circuit is ______.
Which of the following statements about a series LCR circuit connected to an ac source is correct?
