Advertisements
Advertisements
प्रश्न
A series LCR circuit with R = 20 Ω, L = 1.5 H and C = 35 µF is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?
Advertisements
उत्तर
At resonance, the frequency of the supply power equals the natural frequency of the given LCR circuit.
Resistance, R = 20 Ω
Inductance, L = 1.5 H
Capacitance, C = 35 μF = 35 × 10−6 F
AC supply voltage to the LCR circuit, V = 200 V
Impedance of the circuit is given by the relation,
`"Z" = sqrt("R"^2 + (ω"L" - 1/(ω"C"))^2)`
At resonance, ωL = `1/(ω"C")`
∴ Z = R = 20 Ω
Current in the circuit can be calculated as:
`"I" = "V"/"Z"`
= `200/20`
= 10 A
Hence, the average power transferred to the circuit in one complete cycle = VI = 200 × 10 = 2000 W.
APPEARS IN
संबंधित प्रश्न
A source of ac voltage v = v0 sin ωt, is connected across a pure inductor of inductance L. Derive the expressions for the instantaneous current in the circuit. Show that average power dissipated in the circuit is zero.
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.
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.
What will be the potential difference in the circuit when direct current is passed through the circuit?
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.
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.
If an LCR series circuit is connected to an ac source, then at resonance the voltage across ______.
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 :
To reduce the resonant frequency in an LCR series circuit with a generator
The phase diffn b/w the current and voltage at resonance is
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 LCR circuit containing a resistance of 120 Ω has angular resonance frequency 4 × 105 rad s-1. At resonance the voltage across resistance and inductance are 60 V and 40 V respectively. At what frequency the current in the circuit lags the voltage by 45°. Give answer in ______ × 105 rad s-1.
Draw the phasor diagram for a series LRC circuit connected to an AC source.
A series LCR circuit is connected to an ac source. Using the phasor diagram, derive the expression for the impedance of the circuit.
In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1 µF and resistance R is 100Ω. The frequency at which resonance occurs is ______.
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 ______.
