Advertisements
Advertisements
Question
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.
Options
a and b
b and c
c and d
a and d
Advertisements
Solution
a and d
Explanation:
Compare the given circuit by predicting the variation in their reactances with frequency. So, that then we can decide the elements.
Reactance of an inductor of inductance L is XL = 2πvL, where v is the frequency of the AC circuit.
XC = Reactance of the capacitive circuit = `1/(2pi fC)`
With an increase in frequency `(f)` of an AC circuit, R remains constant, inductive reactance (XL) increases and capacitive reactance (XC) decreases.
For an L-C-R circuit,
Z = Impedance of the circuit
= `sqrt(R^2 + (X_L - X_C)^2)`
= `sqrt(R^2 + (2pivL - 1/(2pivC)^2)`
As frequency (v) increases, Z decreases and at certain value of the frequency known as resonant frequency (v0), impedance Z is minimum that is Zmin = R current varies inversely with impedance and at Zmin current is maximum.
APPEARS IN
RELATED QUESTIONS
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.
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.
An L-R circuit has L = 1.0 H and R = 20 Ω. It is connected across an emf of 2.0 V at t = 0. Find di/dt at (a) t = 100 ms, (b) t = 200 ms and (c) t = 1.0 s.
An inductor-coil of inductance 17 mH is constructed from a copper wire of length 100 m and cross-sectional area 1 mm2. Calculate the time constant of the circuit if this inductor is joined across an ideal battery. The resistivity of copper = 1.7 × 10−8 Ω-m.
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.
A constant current exists in an inductor-coil connected to a battery. The coil is short-circuited and the battery is removed. Show that the charge flown through the coil after the short-circuiting is the same as that which flows in one time constant before the short-circuiting.
(i) An a.c. source of emf ε = 200 sin omegat is connected to a resistor of 50 Ω . calculate :
(1) Average current (`"I"_("avg")`)
(2) Root mean square (rms) value of emf
(ii) State any two characteristics of resonance in an LCR series circuit.
In a series, LCR circuit, obtain an expression for the resonant frequency,
Answer the following question.
What is the phase difference between the voltages across the inductor and the capacitor at resonance in the LCR circuit?
Derive an expression for the average power dissipated in a series LCR circuit.
Choose the correct answer from given options
The phase difference between the current and the voltage in series LCR circuit at resonance is
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.
If an LCR series circuit is connected to an ac source, then at resonance the voltage across ______.
To reduce the resonant frequency in an LCR series circuit with a generator
A series LCR circuit containing 5.0 H inductor, 80 µF capacitor and 40 Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be ______.
In series LCR circuit, the plot of Imax vs ω is shown in figure. Find the bandwidth and mark in the figure.
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.
A series LCR circuit is connected to an ac source. Using the phasor diagram, derive the expression for the impedance of the circuit.
