Advertisements
Advertisements
Question
The figure shows a series LCR circuit with L = 10.0 H, C = 40 μF, R = 60 Ω connected to a variable frequency 240 V source, calculate
(i) the angular frequency of the source which drives the circuit at resonance,
(ii) the current at the resonating frequency,
(iii) the rms potential drop across the inductor at resonance.
Solution
(i) Resonant angular frequency
`omega_0 = 1/(sqrt(LC)) = 1/sqrt(10 xx 40 xx 10^6)`
`= 1/(sqrt (400 xx 10^-6 ))= 1/(20 xx 10^-3)`
`=1000/20`
`= 50 \text {rads}^-1`
(ii) At resonant frequency, we know that the inductive reactance cancels out the capacitive reactance.
The impedance = Z = 60Ω the value of resistance
The current amplitude at resonant frequency
`I_0 = E_0/Z = sqrt(2E_v)/R = (sqrt2 xx 240)/60`
` = 339.36/60 = 5.66A`
(iii) The R.M.S. value of current
`I_v = I_0/sqrt2 = 5.66/sqrt2 = 4A`
For R.M.S potential drop across inductor
`V_1 = I_VX_L`
`= I_V xx omega L`
`= 4 xx 50 xx 10`
`= 200 xx 10`
`= 2000 V`
APPEARS IN
RELATED QUESTIONS
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.
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?
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.
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?
A series LCR circuit containing a 5.0 H inductor, 80 µF capacitors, and 40 Ω resistor is connected to a 230 V variable frequency ac source. The angular frequencies of the source at which power is transferred to the circuit are half the power at the resonant angular frequency are likely to be ______.
As the frequency of an ac circuit increases, the current first increases and then decreases. What combination of circuit elements is most likely to comprise the circuit?
- Inductor and capacitor.
- Resistor and inductor.
- Resistor and capacitor.
- Resistor, inductor and capacitor.
A coil of 0.01 henry inductance and 1 ohm resistance is connected to 200 volt, 50 Hz ac supply. Find the impedance of the circuit and time lag between max. alternating voltage and current.
Which of the following statements about a series LCR circuit connected to an ac source is correct?
Three students, X, Y and Z performed an experiment for studying the variation of a.c. with frequency in a series LCR circuit and obtained the graphs as shown below. They all used
- an AC source of the same emf and
- inductance of the same value.
- Who used minimum resistance?
- In which case will the quality Q factor be maximum?
- What did the students conclude about the nature of impedance at resonant frequency (f0)?
- An ideal capacitor is connected across 220V, 50Hz, and 220V, 100Hz supplies. Find the ratio of current flowing through it in the two cases.
