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
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?
What will be the potential difference in the circuit when direct current is passed through the circuit?
Figure shows a series LCR circuit connected to a variable frequency 230 V source. L = 5.0 H, C = 80 µF, R = 40 Ω.
- Determine the source frequency which drives the circuit in resonance.
- Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.
- Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency.
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.
A coil of 40 henry inductance is connected in series with a resistance of 8 ohm and the combination is joined to the terminals of a 2 volt battery. The time constant of the circuit is ______.
The resonant frequency of a RF oscillator is 1 MHz and its bandwidth is 10 kHz. The quality factor will be :
Which of the following components of an LCR circuit, with a.c. supply, dissipates energy?
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.
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.
Select the most appropriate option with regard to resonance in a series LCR circuit.
